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Journal articles on the topic 'T cohomology'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Cobb, Sarah. "Infinite-dimensional cohomology of SL2(Z[t,t−1])." Journal of Algebra 462 (September 2016): 181–96. http://dx.doi.org/10.1016/j.jalgebra.2016.05.017.

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2

BUNKE, ULRICH, and THOMAS SCHICK. "ON THE TOPOLOGY OF T-DUALITY." Reviews in Mathematical Physics 17, no. 01 (2005): 77–112. http://dx.doi.org/10.1142/s0129055x05002315.

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We study a topological version of the T-duality relation between pairs consisting of a principal U(1)-bundle equipped with a degree-three integral cohomology class. We describe the homotopy type of a classifying space for such pairs and show that it admits a selfmap which implements a T-duality transformation. We give a simple derivation of a T-duality isomorphism for certain twisted cohomology theories. We conclude with some explicit computations of twisted K-theory groups and discuss an example of iterated T-duality for higher-dimensional torus bundles.

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3

Lorestani, Keivan Borna, Parviz Sahandi, and Siamak Yassemi. "Artinian Local Cohomology Modules." Canadian Mathematical Bulletin 50, no. 4 (2007): 598–602. http://dx.doi.org/10.4153/cmb-2007-058-8.

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AbstractLet R be a commutative Noetherian ring, α an ideal of R and M a finitely generated R-module. Let t be a non-negative integer. It is known that if the local cohomology module is finitely generated for all i < t, then is finitely generated. In this paper it is shown that if is Artinian for all i < t, then need not be Artinian, but it has a finitely generated submodule N such that /N is Artinian.

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4

Mafi, Amir. "On the Finiteness Results of the Generalized Local Cohomology Modules." Algebra Colloquium 16, no. 02 (2009): 325–32. http://dx.doi.org/10.1142/s1005386709000315.

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Let 𝔞 be an ideal of a commutative Noetherian local ring R, and let M and N be two finitely generated R-modules. Let t be a positive integer. It is shown that if the support of the generalized local cohomology module [Formula: see text] is finite for all i < t, then the set of associated prime ideals of the generalized local cohomology module [Formula: see text] is finite. Also, if the support of the local cohomology module [Formula: see text] is finite for all i < t, then the set [Formula: see text] is finite. Moreover, we prove that gdepth (𝔞+ Ann (M),N) is the least integer t such tha

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5

Sato, Takashi. "The $T$ -equivariant integral cohomology ring of $F_{4}/T$." Kyoto Journal of Mathematics 54, no. 4 (2014): 703–26. http://dx.doi.org/10.1215/21562261-2801786.

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6

ANANTHARAMAN-DELAROCHE, CLAIRE. "Cohomology of property T groupoids and applications." Ergodic Theory and Dynamical Systems 25, no. 4 (2005): 977–1013. http://dx.doi.org/10.1017/s0143385704000884.

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7

Nakagawa, Masaki. "The integral cohomology ring of $E_7/T$." Journal of Mathematics of Kyoto University 41, no. 2 (2001): 303–21. http://dx.doi.org/10.1215/kjm/1250517635.

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8

Fernós, Talia, Alain Valette, and Florian Martin. "Reduced 1-cohomology and relative property (T)." Mathematische Zeitschrift 270, no. 3-4 (2010): 613–26. http://dx.doi.org/10.1007/s00209-010-0815-1.

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9

Baues, H. J., and F. Muro. "Cohomologically triangulated categories I." Journal of K-Theory 1, no. 1 (2008): 3–48. http://dx.doi.org/10.1017/is007011018jkt019.

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AbstractWe introduce cohomologically triangulated categories as triples (A,t,▽) given by an additive category A, an additive equivalence t:AA and a cohomology class ▽ in the translation cohomology H3(A,t). A stable homotopy theory C with A = HoC yields such a triple and the class of distinguished triangles in A is deduced from ▽.

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10

Crooks, Peter, and Tyler Holden. "Generalized Equivariant Cohomology and Stratifications." Canadian Mathematical Bulletin 59, no. 3 (2016): 483–96. http://dx.doi.org/10.4153/cmb-2016-032-5.

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AbstractFor T a compact torus and a generalized T-equivariant cohomology theory, we provide a systematic framework for computing in the context of equivariantly stratified smooth complex projective varieties. This allows us to explicitly compute as an (pt)-module when X is a direct limit of smooth complex projective Tℂ-varieties. We perform this computation on the affine Grassmannian of a complex semisimple group.

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11

Lenart, Cristian, Kirill Zainoulline, and Changlong Zhong. "PARABOLIC KAZHDAN–LUSZTIG BASIS, SCHUBERT CLASSES, AND EQUIVARIANT ORIENTED COHOMOLOGY." Journal of the Institute of Mathematics of Jussieu 19, no. 6 (2019): 1889–929. http://dx.doi.org/10.1017/s1474748018000592.

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We study the equivariant oriented cohomology ring $\mathtt{h}_{T}(G/P)$ of partial flag varieties using the moment map approach. We define the right Hecke action on this cohomology ring, and then prove that the respective Bott–Samelson classes in $\mathtt{h}_{T}(G/P)$ can be obtained by applying this action to the fundamental class of the identity point, hence generalizing previously known results of Chow groups by Brion, Knutson, Peterson, Tymoczko and others. Our main result concerns the equivariant oriented cohomology theory $\mathfrak{h}$ corresponding to the 2-parameter Todd genus. We giv

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12

Hayami, Takao. "On Hochschild cohomology ring and integral cohomology ring for the semidihedral group." International Journal of Algebra and Computation 28, no. 02 (2018): 257–90. http://dx.doi.org/10.1142/s0218196718500121.

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We will determine the ring structure of the Hochschild cohomology [Formula: see text] of the integral group ring of the semidihedral group [Formula: see text] of order [Formula: see text] for arbitrary integer [Formula: see text] by giving the precise description of the integral cohomology ring [Formula: see text] and by using a method similar to [T. Hayami, Hochschild cohomology ring of the integral group ring of the semidihedral [Formula: see text]-group, Algebra Colloq. 18 (2011) 241–258].

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13

GARCÍA DEL MORAL, MARÍA PILAR, JOSELEN PEÑA, and ALVARO RESTUCCIA. "T-DUALITY INVARIANCE OF THE SUPERMEMBRANE." International Journal of Geometric Methods in Modern Physics 10, no. 08 (2013): 1360010. http://dx.doi.org/10.1142/s0219887813600104.

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We show that the supermembrane theory compactified on a torus is invariant under T-duality. There are two different topological sectors of the compactified supermembrane (M2) classified according to a vanishing or nonvanishing second cohomology class. We find the explicit T-duality transformation that acts locally on the supermembrane theory and we show that it is an exact symmetry of the theory. We give a global interpretation of the T-duality in terms of bundles. It has a natural description in terms of the cohomology of the base manifold and the homology of the target torus. We show that in

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14

Nakagawa, Masaki. "The integral cohomology ring of E 8 / T." Proceedings of the Japan Academy, Series A, Mathematical Sciences 86, no. 3 (2010): 64–68. http://dx.doi.org/10.3792/pjaa.86.64.

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15

Alesker, Semyon, and Maxim Braverman. "Cohomology of a Hamiltonian $T$-space with involution." Journal of Symplectic Geometry 14, no. 1 (2016): 325–40. http://dx.doi.org/10.4310/jsg.2016.v14.n1.a13.

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16

Knudson, Kevin P. "Congruence Subgroups and Twisted Cohomology ofSLn(F[t])." Journal of Algebra 207, no. 2 (1998): 695–721. http://dx.doi.org/10.1006/jabr.1998.7455.

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17

Payrovi, Sh, S. Babaei, and I. Khalili-Gorji. "Bass numbers of generalized local cohomology modules." Publications de l'Institut Math?matique (Belgrade) 97, no. 111 (2015): 233–38. http://dx.doi.org/10.2298/pim140620001p.

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Let R be a Noetherian ring, M a finitely generated R-module and N an arbitrary R-module. We consider the generalized local cohomology modules, with respect to an arbitrary ideal I of R, and prove that, for all nonnegative integers r, t and all p ? Spec(R) the Bass number ?r(p,HtI (M,N)) is bounded above by ?tj=0?r(p, t?jExtR (M,HjI (N))). A corollary is that Ass (HtI (M,N)? Utj=0 Ass (t?jExtR (M,HjI(N))). In a slightly different direction, we also present some well known results about generalized local cohomology modules.

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18

GOLDIN, REBECCA F., and MEGUMI HARADA. "ORBIFOLD COHOMOLOGY OF HYPERTORIC VARIETIES." International Journal of Mathematics 19, no. 08 (2008): 927–56. http://dx.doi.org/10.1142/s0129167x08004947.

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Hypertoric varieties are hyperkähler analogues of toric varieties, and are constructed as abelian hyperkähler quotients T*ℂn//// T of a quaternionic affine space. Just as symplectic toric orbifolds are determined by labelled polytopes, orbifold hypertoric varieties are intimately related to the combinatorics of hyperplane arrangements. By developing hyperkähler analogues of symplectic techniques developed by Goldin, Holm, and Knutson, we give an explicit combinatorial description of the Chen–Ruan orbifold cohomology of an orbifold hypertoric variety in terms of the combinatorial data of a rati

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19

SHCHIGOLEV, VLADIMIR. "BASES OF -EQUIVARIANT COHOMOLOGY OF BOTT–SAMELSON VARIETIES." Journal of the Australian Mathematical Society 104, no. 1 (2017): 80–126. http://dx.doi.org/10.1017/s1446788717000064.

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We construct combinatorial bases of the $T$-equivariant cohomology $H_{T}^{\bullet }(\unicode[STIX]{x1D6F4},k)$ of the Bott–Samelson variety $\unicode[STIX]{x1D6F4}$ under some mild restrictions on the field of coefficients $k$. These bases allow us to prove the surjectivity of the restrictions $H_{T}^{\bullet }(\unicode[STIX]{x1D6F4},k)\rightarrow H_{T}^{\bullet }(\unicode[STIX]{x1D70B}^{-1}(x),k)$ and $H_{T}^{\bullet }(\unicode[STIX]{x1D6F4},k)\rightarrow H_{T}^{\bullet }(\unicode[STIX]{x1D6F4}\setminus \unicode[STIX]{x1D70B}^{-1}(x),k)$, where $\unicode[STIX]{x1D70B}:\unicode[STIX]{x1D6F4}\

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20

Baues, H. J., and F. Muro. "Cohomologically triangulated categories II." Journal of K-Theory 3, no. 1 (2008): 1–52. http://dx.doi.org/10.1017/is008007021jkt061.

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AbstractA cohomologically triangulated category is an additive categoryAtogether with a translation functortand a cohomology class Δ ∈H3(A,t) such that any good translation track category representing Δ is a triangulated track category. In this paper we give purely cohomological conditions on Δ which imply that (A,t,Δ) is a cohomologically triangulated category, avoiding the use of track categories. This yields a purely cohomological characterization of triangulated cohomology classes.

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21

Dasgupta, Jyoti, Bivas Khan, and Vikraman Uma. "Cohomology of torus manifold bundles." Mathematica Slovaca 69, no. 3 (2019): 685–98. http://dx.doi.org/10.1515/ms-2017-0257.

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Abstract Let X be a 2n-dimensional torus manifold with a locally standard T ≅ (S1)n action whose orbit space is a homology polytope. Smooth complete complex toric varieties and quasitoric manifolds are examples of torus manifolds. Consider a principal T-bundle p : E → B and let π : E(X) → B be the associated torus manifold bundle. We give a presentation of the singular cohomology ring of E(X) as a H*(B)-algebra and the topological K-ring of E(X) as a K*(B)-algebra with generators and relations. These generalize the results in [17] and [19] when the base B = pt. These also extend the results in

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22

BARAGLIA, DAVID. "CONFORMAL COURANT ALGEBROIDS AND ORIENTIFOLD T-DUALITY." International Journal of Geometric Methods in Modern Physics 10, no. 02 (2012): 1250084. http://dx.doi.org/10.1142/s0219887812500843.

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We introduce conformal Courant algebroids, a mild generalization of Courant algebroids in which only a conformal structure rather than a bilinear form is assumed. We introduce exact conformal Courant algebroids and show they are classified by pairs (L, H) with L a flat line bundle and H ∈ H3(M, L) a degree 3 class with coefficients in L. As a special case gerbes for the crossed module (U(1) → ℤ2) can be used to twist TM ⊕ T*M into a conformal Courant algebroid. In the exact case there is a twisted cohomology which is 4-periodic if L2 = 1. The structure of Conformal Courant algebroids on circle

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23

LUZ, RICHARD U., and NATHAN M. DOS SANTOS. "Cohomology-free diffeomorphisms of low-dimension tori." Ergodic Theory and Dynamical Systems 18, no. 4 (1998): 985–1006. http://dx.doi.org/10.1017/s0143385798108222.

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We study cohomology-free (c.f.) diffeomorphisms of the torus $T^n$. A diffeomorphism is c.f. if every smooth function $f$ on $T^n$ is cohomologous to a constant $f_0$, i.e. there exists a $C^{\infty}$ function $h$ so that $h-h\circ\varphi=f-f_0$. We show that the only c.f. diffeomorphisms of $T^n$, $1\le n\le3$, are the smooth conjugations of Diophantine translations. For $n=4$, we prove the same result for c.f. orientation-preserving diffeomorphisms.

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24

Goresky, Mark, and Robert MacPherson. "On the Spectrum of the Equivariant Cohomology Ring." Canadian Journal of Mathematics 62, no. 2 (2010): 262–83. http://dx.doi.org/10.4153/cjm-2010-016-4.

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AbstractIf an algebraic torusTacts on a complex projective algebraic varietyX, then the affine scheme SpecH*T(X; ℂ) associated with the equivariant cohomology is often an arrangement of linear subspaces of the vector spaceHT2(X; ℂ). In many situations the ordinary cohomology ring ofXcan be described in terms of this arrangement.

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25

Nakamura, Tsutomu. "On ideals preserving generalized local cohomology modules." Journal of Algebra and Its Applications 15, no. 01 (2015): 1650019. http://dx.doi.org/10.1142/s0219498816500195.

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Let R be a commutative Noetherian ring, 𝔞 an ideal of R and M, N two finitely generated R-modules. Let t be a positive integer or ∞. We denote by Ωt the set of ideals 𝔠 such that [Formula: see text] for all i < t. First, we show that there exists the ideal 𝔟t which is the largest in Ωt and [Formula: see text]. Next, we prove that if 𝔡 is an ideal such that 𝔞 ⊆ 𝔡 ⊆ 𝔟t, then [Formula: see text] for all i < t.

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26

Bui, Cam Thi Hong, and Tri Minh Nguyen. "On the cominimaxness of generalized local cohomology modules." Science and Technology Development Journal 23, no. 1 (2020): 479–83. http://dx.doi.org/10.32508/stdj.v23i1.1696.

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The local cohomology theory plays an important role in commutative algebra and algebraic geometry. The I-cofiniteness of local cohomology modules is one of interesting properties which has been studied by many mathematicians. The I-cominimax modules is an extension of I-cofinite modules which was introduced by Hartshorne. An R-module M is I-cominimax if Supp_R(M)\subseteq V(I) and Ext^i_R(R/I,M) is minimax for all i\ge 0. In this paper, we show some conditions such that the generalized local cohomology module H^i_I(M,N) is I-cominimax for all i\ge 0. We show that if H^i_I(M,K) is I-cofinite fo

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27

Eguchi, Tohru, Kentaro Hori, and Chuan-Sheng Xiong. "Gravitational Quantum Cohomology." International Journal of Modern Physics A 12, no. 09 (1997): 1743–82. http://dx.doi.org/10.1142/s0217751x97001146.

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We discuss how the theory of quantum cohomology may be generalized to "gravitational quantum cohomology" by studying topological σ models coupled to two-dimensional gravity. We first consider σ models defined on a general Fano manifold M (manifold with a positive first Chern class) and derive new recursion relations for its two-point functions. We then derive bi-Hamiltonian structures of the theories and show that they are completely integrable at least at the level of genus 0. We next consider the subspace of the phase space where only a marginal perturbation (with a parameter t) is turned on

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28

CHU, LIZHONG. "COFINITENESS AND FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES." Bulletin of the Australian Mathematical Society 80, no. 2 (2009): 244–50. http://dx.doi.org/10.1017/s0004972709000240.

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AbstractLet I be an ideal of a commutative Noetherian local ring R, and M and N two finitely generated modules. Let t be a positive integer. We mainly prove that (i) if HIi(M,N) is Artinian for all i<t, then HIi(M,N) is I-cofinite for all i<t and Hom(R/I,HIt(M,N)) is finitely generated; (ii) if d=pd(M)<∞ and dim N=n<∞, then HId+n(M,N) is I-cofinite. We also prove that if M is a nonzero cyclic R-module, then HIi(N) is finitely generated for all i<t if and only if HIi(M,N) is finitely generated for all i<t.

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29

Goldin, R. F., and S. Martin. "Cohomology Pairings on the Symplectic Reduction of Products." Canadian Journal of Mathematics 58, no. 2 (2006): 362–80. http://dx.doi.org/10.4153/cjm-2006-015-3.

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AbstractLet M be the product of two compact Hamiltonian T-spaces X and Y . We present a formula for evaluating integrals on the symplectic reduction of M by the diagonal T action. At every regular value of the moment map for X × Y, the integral is the convolution of two distributions associated to the symplectic reductions of X by T and of Y by T. Several examples illustrate the computational strength of this relationship. We also prove a linear analogue which can be used to find cohomology pairings on toric orbifolds.

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30

Braverman, Maxim. "Symplectic cutting of Kähler manifolds." Journal für die reine und angewandte Mathematik (Crelles Journal) 1999, no. 508 (1999): 85–98. http://dx.doi.org/10.1515/crll.1999.508.85.

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Abstract We obtain estimates on the character of the cohomology of an S1-equivariant holomorphic vector bundle over a Kähler manifold M in terms of the cohomology of the Lerman symplectic cuts and the symplectic reduction of M. In particular, we prove and extend inequalities conjectured by Wu and Zhang. The proof is based on constructing a flat family of complex spaces Mt (t ∈ ℂ) such that Mt is isomorphic to M for t ≠ 0, while M0 is a singular reducible complex space, whose irreducible components are the Lerman symplectic cuts.

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31

Duan, Haibao, and Xuezhi Zhao. "Schubert presentation of the cohomology ring of flag manifolds." LMS Journal of Computation and Mathematics 18, no. 1 (2015): 489–506. http://dx.doi.org/10.1112/s1461157015000133.

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Let $G$ be a compact connected Lie group with a maximal torus $T$. In the context of Schubert calculus we present the integral cohomology $H^{\ast }(G/T)$ by a minimal system of generators and relations.

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32

Mafi, A., and H. Saremi. "Generalized Regular Sequence and Finiteness of Local Cohomology Modules." Algebra Colloquium 15, no. 03 (2008): 457–62. http://dx.doi.org/10.1142/s1005386708000436.

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Let R be a commutative Noetherian local ring, 𝔞 an ideal of R, and M a finitely generated generalized f-module. Let t be a positive integer such that [Formula: see text] and t > dim M - dim M/𝔞M. In this paper, we prove that there exists an ideal 𝔟 ⊇ 𝔞 such that (1) dim M - dim M/𝔟M = t; and (2) the natural homomorphism [Formula: see text] is an isomorphism for all i > t and it is surjective for i = t. Also, we show that if [Formula: see text] is a finite set for all i < t, then there exists an ideal 𝔟 of R such that dim R/𝔟 ≤ 1 and [Formula: see text] for all i < t.

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33

Saremi, Hero, and Amir Mafi. "On the Finiteness Dimension of Local Cohomology Modules." Algebra Colloquium 21, no. 03 (2014): 517–20. http://dx.doi.org/10.1142/s1005386714000455.

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Let R be a commutative Noetherian ring, 𝔞 an ideal of R, and M a non-zero finitely generated R-module. Let t be a non-negative integer. In this paper, it is shown that [Formula: see text] for all i < t if and only if there exists an ideal 𝔟 of R such that dim R/𝔟 ≤ 1 and [Formula: see text] for all i < t. Moreover, we prove that [Formula: see text] for all i.

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34

DAO, HAILONG, and PHAM HUNG QUY. "ON THE ASSOCIATED PRIMES OF LOCAL COHOMOLOGY." Nagoya Mathematical Journal 237 (February 5, 2018): 1–9. http://dx.doi.org/10.1017/nmj.2017.44.

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Let $R$ be a commutative Noetherian ring of prime characteristic $p$. In this paper, we give a short proof using filter regular sequences that the set of associated prime ideals of $H_{I}^{t}(R)$ is finite for any ideal $I$ and for any $t\geqslant 0$ when $R$ has finite $F$-representation type or finite singular locus. This extends a previous result by Takagi–Takahashi and gives affirmative answers for a problem of Huneke in many new classes of rings in positive characteristic. We also give a criterion about the singularities of $R$ (in any characteristic) to guarantee that the set $\operatorn

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35

SADUN, LORENZO. "Exact regularity and the cohomology of tiling spaces." Ergodic Theory and Dynamical Systems 31, no. 6 (2011): 1819–34. http://dx.doi.org/10.1017/s0143385710000611.

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AbstractExact regularity was introduced recently as a property of homological Pisot substitutions in one dimension. In this paper, we consider the analog of exact regularity for arbitrary tiling spaces. Let T be a d-dimensional repetitive tiling, and let Ω be its hull. If Ȟd(Ω,ℚ)=ℚk, then there exist k patches each of whose appearances governs the number of appearances of every other patch. This gives uniform estimates on the convergence of all patch frequencies to the ergodic limit. If the tiling T comes from a substitution, then we can quantify that convergence rate. If T is also one dimensi

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36

Moskowitz, Martin. "Bilinear forms and 2-dimensional cohomology." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 41, no. 2 (1986): 165–79. http://dx.doi.org/10.1017/s1446788700033589.

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AbstractThis paper calculates the central Borel 2 cocycles for certain 2-step nilpotent Lie groups G with values in the injectives A of the category of 2nd countable locally compact abelian groups. The G's include, among others, all groups locally isomorphic to a Heisenberg group. The A's are direct sums of vector groups and (possibly infinite dimensional) tori, and in particular include R, T, and Cx. The main results are as follows.(4.1) Every symmetric central 2 cocycle is trivial.(4.2) Every central 2 cocycle is cohomologous with a skew symmetric bimultiplicative one (which is necessarily j

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37

Liu, Ming, and Xia Zhang. "Twisted Weyl Groups of Compact Lie Groups and Nonabelian Cohomology." Mathematics 8, no. 1 (2019): 21. http://dx.doi.org/10.3390/math8010021.

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Given a compact connected Lie group G with an S 1 -module structure and a maximal compact torus T of G S 1 , we define twisted Weyl group W ( G , S 1 , T ) of G associated to S 1 -module and show that two elements of T are δ -conjugate if and only if they are in one W ( G , S 1 , T ) -orbit. Based on this, we prove that the natural map W ( G , S 1 , T ) \ H 1 ( S 1 , T ) → H 1 ( S 1 , G ) is bijective, which reduces the calculation for the nonabelian cohomology H 1 ( S 1 , G ) .

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38

ANGELLA, DANIELE, and ADRIANO TOMASSINI. "ON THE COHOMOLOGY OF ALMOST-COMPLEX MANIFOLDS." International Journal of Mathematics 23, no. 02 (2012): 1250019. http://dx.doi.org/10.1142/s0129167x11007604.

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Following [T.-J. Li and W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.17(4) (2009) 651–683], we continue to study the link between the cohomology of an almost-complex manifold and its almost-complex structure. In particular, we apply the same argument in [T.-J. Li and W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.17(4) (2009) 651–683] and the results obtained by [D. Sullivan, Cycles for the dynamical study of foliated mani

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39

Wang, Shengxiang, Xiaohui Zhang та Shuangjian Guo. "Derivations and Deformations of δ-Jordan Lie Supertriple Systems". Advances in Mathematical Physics 2019 (11 липня 2019): 1–15. http://dx.doi.org/10.1155/2019/3295462.

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Let T be a δ-Jordan Lie supertriple system. We first introduce the notions of generalized derivations and representations of T and present some properties. Also, we study the low-dimensional cohomology and the coboundary operator of T, and then we investigate the deformations and Nijenhuis operators of T by choosing some suitable cohomologies.

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40

Packer, Judith A. "Moore Cohomology and Central Twisted Crossed Product C*-Algebras." Canadian Journal of Mathematics 48, no. 1 (1996): 159–74. http://dx.doi.org/10.4153/cjm-1996-007-6.

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AbstractLet G be a locally compact second countable group, let X be a locally compact second countable Hausdorff space, and view C(X, T) as a trivial G-module. For G countable discrete abelian, we construct an isomorphism between the Moore cohomology group Hn(G, C(X, T)) and the direct sum Ext(Hn-1(G), Ȟl(βX, Ζ)) ⊕ C(X, Hn(G, T)); here Ȟ1 (βX, Ζ) denotes the first Čech cohomology group of the Stone-Čech compactification of X, βX, with integer coefficients. For more general locally compact second countable groups G, we discuss the relationship between the Moore group H2(G, C(X, T)), the set of

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41

Varbaro, Matteo. "Cohomological and projective dimensions." Compositio Mathematica 149, no. 7 (2013): 1203–10. http://dx.doi.org/10.1112/s0010437x12000899.

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AbstractLet $\mathfrak{a}$ be a homogeneous ideal of a polynomial ring $R$ in $n$ variables over a field $\mathbb{k}$. Assume that $\mathrm{depth} (R/ \mathfrak{a})\geq t$, where $t$ is some number in $\{ 0, \ldots , n\} $. A result of Peskine and Szpiro says that if $\mathrm{char} (\mathbb{k})\gt 0$, then the local cohomology modules ${ H}_{\mathfrak{a}}^{i} (M)$ vanish for all $i\gt n- t$ and all $R$-modules $M$. In characteristic $0$, there are counterexamples to this for all $t\geq 4$. On the other hand, when $t\leq 2$, by exploiting classical results of Grothendieck, Lichtenbaum, Hartshor

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42

Galatan, Alin, and Sorin Popa. "SMOOTH BIMODULES AND COHOMOLOGY OF II1 FACTORS." Journal of the Institute of Mathematics of Jussieu 16, no. 1 (2015): 155–87. http://dx.doi.org/10.1017/s1474748015000122.

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We prove that, under rather general conditions, the 1-cohomology of a von Neumann algebra $M$ with values in a Banach $M$-bimodule satisfying a combination of smoothness and operatorial conditions vanishes. For instance, we show that, if $M$ acts normally on a Hilbert space ${\mathcal{H}}$ and ${\mathcal{B}}_{0}\subset {\mathcal{B}}({\mathcal{H}})$ is a norm closed $M$-bimodule such that any $T\in {\mathcal{B}}_{0}$ is smooth (i.e., the left and right multiplications of $T$ by $x\in M$ are continuous from the unit ball of $M$ with the $s^{\ast }$-topology to ${\mathcal{B}}_{0}$ with its norm),

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43

Leal, Isabel. "On the ramification of étale cohomology groups." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 749 (2019): 295–304. http://dx.doi.org/10.1515/crelle-2016-0035.

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Abstract Let K be a complete discrete valuation field whose residue field is perfect and of positive characteristic, let X be a connected, proper scheme over \mathcal{O}_{K} , and let U be the complement in X of a divisor with simple normal crossings. Assume that the pair (X,U) is strictly semi-stable over \mathcal{O}_{K} of relative dimension one and K is of equal characteristic. We prove that, for any smooth \ell -adic sheaf \mathcal{G} on U of rank one, at most tamely ramified on the generic fiber, if the ramification of \mathcal{G} is bounded by t+ for the logarithmic upper ramification gr

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44

ZAMANI, NASER. "RESULTS ON LOCAL COHOMOLOGY OF WEAKLY LASKERIAN MODULES." Journal of Algebra and Its Applications 10, no. 02 (2011): 303–8. http://dx.doi.org/10.1142/s0219498811004586.

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Let R be a commutative Noetherian ring, 𝔞 be an ideal of R and M be an arbitrary R-module. In this paper, among other things, we show that if, for a non-negative integer t, the R-module [Formula: see text] is weakly Laskerian and [Formula: see text] is 𝔞-weakly cofinite for all i < t, then, for any weakly Laskerian submodule U of [Formula: see text], the R-module [Formula: see text] is weakly Laskerian. As a consequence the set of associated primes of [Formula: see text] is finite.

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45

SAREMI, HERO, and AMIR MAFI. "FINITENESS DIMENSION AND BASS NUMBERS OF GENERALIZED LOCAL COHOMOLOGY MODULES." Journal of Algebra and Its Applications 12, no. 07 (2013): 1350036. http://dx.doi.org/10.1142/s0219498813500369.

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Let R be a commutative Noetherian ring, 𝔞 an ideal of R, and M, N two nonzero finitely generated R-modules. Let t be a non-negative integer. It is shown that dim Supp [Formula: see text] for all i < t if and only if there exists an ideal 𝔟 of R such that dim R/𝔟 ≤ 1 and [Formula: see text] for all i < t. As a consequence all Bass numbers and all Betti numbers of generalized local cohomology modules [Formula: see text] are finite for all i < t, provided that the projective dimension pd (M) is finite.

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46

Chu, Lizhong. "On the Artinianness of Graded Local Cohomology Modules." Algebra Colloquium 17, no. 04 (2010): 699–704. http://dx.doi.org/10.1142/s1005386710000660.

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Let R = ⨁n≥ 0 Rn be a homogeneous noetherian ring with local base ring [Formula: see text], and N a finitely generated graded R-module. Let [Formula: see text] be the i-th local cohomology module of N with respect to R+ := ⨁n > 0 Rn. Let t be the largest integer such that [Formula: see text] is not minimax. We prove that [Formula: see text] is [Formula: see text]-coartinian for any i > t, and [Formula: see text] is artinian. Let s be the first integer such that [Formula: see text] is not minimax. We show that for any i ≤ s, the graded module [Formula: see text] is artinian.

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47

Bondarko, M. V. "Differential graded motives: weight complex, weight filtrations and spectral sequences for realizations; Voevodsky versus Hanamura." Journal of the Institute of Mathematics of Jussieu 8, no. 1 (2008): 39–97. http://dx.doi.org/10.1017/s147474800800011x.

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AbstractWe describe explicitly the Voevodsky's triangulated category of motives $\operatorname{DM}^{\mathrm{eff}}_{\mathrm{gm}}$ (and give a ‘differential graded enhancement’ of it). This enables us to able to verify that DMgm ℚ is (anti)isomorphic to Hanamura's $\mathcal{D}$(k).We obtain a description of all subcategories (including those of Tate motives) and of all localizations of $\operatorname{DM}^{\mathrm{eff}}_{\mathrm{gm}}$. We construct a conservative weight complex functor $t:\smash{\operatorname{DM}^{\mathrm{eff}}_{\mathrm{gm}}}\to\smash{K^{\mathrm{b}}(\operatorname{Chow}^{\mathrm{e

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48

Saremi, Hero. "Matlis Duality and Finiteness Properties of Generalized Local Cohomology Modules." Algebra Colloquium 17, no. 04 (2010): 637–46. http://dx.doi.org/10.1142/s1005386710000611.

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Let [Formula: see text] be an ideal of a commutative Noetherian local ring [Formula: see text] and M, N be two finitely generated R-modules such that M is of finite projective dimension n. Let t be a positive integer. We show that if there exists a regular sequence [Formula: see text] with [Formula: see text] and the i-th local cohomology module [Formula: see text] of N with respect to [Formula: see text] is zero for all i > t, then [Formula: see text], where D(-):= Hom R(-,E). Also, we prove that if N is a Cohen-Macaulay R-module of dimension d, then the generalized local cohomology module

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49

D'Hoker, Eric. "Invariant effective actions, cohomology of homogeneous spaces and anomalies." Nuclear Physics B 451, no. 3 (1995): 725–48. http://dx.doi.org/10.1016/0550-3213(95)00265-t.

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50

Abdalla, E., and K. D. Rothe. "BRST cohomology and vacuum structure of two-dimensional chromodynamics." Physics Letters B 363, no. 1-2 (1995): 85–92. http://dx.doi.org/10.1016/0370-2693(95)01193-t.

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