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Journal articles on the topic 'Cohomologie groupe'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Colliot-Thélène, Jean-Louis. "Troisième groupe de cohomologie non ramifiée des hypersurfaces de Fano." Tunisian Journal of Mathematics 1, no. 1 (January 1, 2019): 47–57. http://dx.doi.org/10.2140/tunis.2019.1.47.

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2

Touzé, Antoine. "Cohomologie du groupe linéaire à coefficients dans les polynômes de matrices." Comptes Rendus Mathematique 345, no. 4 (August 2007): 193–98. http://dx.doi.org/10.1016/j.crma.2007.06.024.

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3

Boissière, Samuel. "Automorphismes naturels de l'espace de Douady de points sur une surface." Canadian Journal of Mathematics 64, no. 1 (February 1, 2012): 3–23. http://dx.doi.org/10.4153/cjm-2011-041-5.

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RésuméOn établit quelques résultats généraux relatifs à la taille du groupe d’automorphismes de l’espace de Douady de points sur une surface, puis on étudie quelques propriétés des automorphismes provenant d’un automorphisme de la surface, en particulier leur action sur la cohomologie et la classification de leurs points fixes.

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4

Harari, David. "Quelques propriétés d’approximation reliées à la cohomologie galoisienne d’un groupe algébrique fini." Bulletin de la Société mathématique de France 135, no. 4 (2007): 549–64. http://dx.doi.org/10.24033/bsmf.2545.

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5

Huyghe, Christine, and Tobias Schmidt. "𝒟-modules arithmétiques sur la variété de drapeaux." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 754 (September 1, 2019): 1–15. http://dx.doi.org/10.1515/crelle-2017-0021.

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Abstract Soient p un nombre premier, V un anneau de valuation discrète complet d’inégales caractéristiques (0,p) , et G un groupe réductif et deployé sur \operatorname{Spec}V . Nous obtenons un théorème de localisation, en utilisant les distributions arithmétiques, pour le faisceau des opérateurs différentiels arithmétiques sur la variété de drapeaux formelle de G. Nous donnons une application à la cohomologie rigide pour des ouverts dans la variété de drapeaux en caractéristique p. Let p be a prime number, V a complete discrete valuation ring of unequal characteristics (0,p) , and G a connected split reductive algebraic group over \operatorname{Spec}V . We obtain a localization theorem, involving arithmetic distributions, for the sheaf of arithmetic differential operators on the formal flag variety of G. We give an application to the rigid cohomology of open subsets in the characteristic p flag variety.

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6

Arabia, Alberto. "Cohomologie T-équivariante de la variété de drapeaux d'un groupe de Kač-Moody." Bulletin de la Société mathématique de France 117, no. 2 (1989): 129–65. http://dx.doi.org/10.24033/bsmf.2116.

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7

Pascal BOYER. "Groupe mirabolique, stratification de Newton raffinée et cohomologie des espaces de Lubin-Tate." Bulletin de la Société mathématique de France 148, no. 1 (2020): 1–23. http://dx.doi.org/10.24033/bsmf.2797.

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8

Tchoudjem, Alexis. "Cohomologie des fibrés en droites sur la compactification magnifique d'un groupe semi-simple adjoint." Comptes Rendus Mathematique 334, no. 6 (January 2002): 441–44. http://dx.doi.org/10.1016/s1631-073x(02)02288-4.

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9

Fargues, Laurent. "G-torseurs en théorie de Hodge p-adique." Compositio Mathematica 156, no. 10 (October 2020): 2076–110. http://dx.doi.org/10.1112/s0010437x20007423.

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RésuméÉtant donné un groupe réductif $G$ sur une extension de degré fini de $\mathbb {Q}_p$ on classifie les $G$-fibrés sur la courbe introduite dans Fargues and Fontaine [Courbes et fibrés vectoriels en théorie de Hodge$p$-adique, Astérisque 406 (2018)]. Le résultat est interprété en termes de l'ensemble $B(G)$ de Kottwitz. On calcule également la cohomologie étale de la courbe à coefficients de torsion en lien avec la théorie du corps de classe local.

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10

Benson, D. J., and V. Franjou. "Séries de compositions de modules instables et injectivité de la cohomologie du groupe ℤ/2." Mathematische Zeitschrift 208, no. 1 (December 1991): 389–99. http://dx.doi.org/10.1007/bf02571535.

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11

Greenlees, J. P. C. "Generalized Eilenberg–Moore spectral sequences for elementary abelian groups and tori." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 1 (July 1992): 77–89. http://dx.doi.org/10.1017/s0305004100070778.

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AbstractIn this note we prove universal coefficient theorems for Borel cohomology and related theories. Whatever other merit this may have the comment of Borel [5] applies ‘ …elle a au moms l'utilité de bien mettre en évidence le rôle fondamental joué dans cette question par la cohomologie des groupes’.Indeed the purpose of the enterprise is to use homological properties of the group cohomology ring H*(BG+) to study properties of G-spaces. Because of the relative simplicity of ordinary cohomology much attention in the proofs and applications is concentrated on change of groups, and on changes in the way the group action is exploited. Nonetheless we are able to adapt the non-equivariant approach of Adams ([1, 2]; see also [3]). Thus the existence of universal coefficient theorems automatically gives Kiinneth theorems as special cases.

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12

OSPEL, CYRILLE. "INVARIANTS OF 3-MANIFOLDS ASSOCIATED TO 3-COCYCLES OF GROUPS." Journal of Knot Theory and Its Ramifications 17, no. 06 (June 2008): 733–70. http://dx.doi.org/10.1142/s0218216508006385.

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We study relations between group cohomologies and 3-manifold invariants. We first give a combinatorial construction of 3-manifold invariants using weight systems. We give examples of weight systems arising from a particular group cohomology. In the second part we show that these invariants can be obtained in a functorial way.

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13

Satoh, Takao. "On the Andreadakis conjecture restricted to the “lower-triangular” automorphism groups of free groups." Journal of Algebra and Its Applications 16, no. 05 (April 12, 2017): 1750099. http://dx.doi.org/10.1142/s0219498817500992.

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In this paper, we consider a certain subgroup [Formula: see text] of the IA-automorphism group of a free group. We determine the images of the [Formula: see text]th Johnson homomorphism restricted to [Formula: see text] for any [Formula: see text] and [Formula: see text]. By using this result, we give an affirmative answer to the Andreadakis conjecture restricted for [Formula: see text]. Namely, we show that the intersection of the Andreadakis–Johnson filtration and [Formula: see text] coincides with the lower central series of [Formula: see text]. In a series of this research, we obtain additional results on the integral (co)homology groups of [Formula: see text]. In particular, we determine the first homology group, and study the cup product of first cohomologies of [Formula: see text]. Furthermore, we construct nontrivial second homology classes of [Formula: see text] by observing its generators and relators, and show that the second cohomology group is not generated by cup products of the first cohomology groups.

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14

Wouters, Tim. "L'invariant de Suslin en caractéristique positive." Journal of K-theory 5, no. 3 (June 2010): 559–602. http://dx.doi.org/10.1017/is010005019jkt117.

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RÉSUMÉPour une k-algèbre simple centrale A d'indice inversible dans k, Suslin a défini un invariant cohomologique de SK1 (A) ‘Sus2’. Dans ce texte, nous généralisons cet invariant à toute k-algèbre simple centrale par un relèvement de la caractéristique positive à la caractéristique 0. Pour pouvoir définir cet invariant, on a besoin des groupes de cohomologie des différentielles logarithmiques de Kato [Kat1].

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15

Sheng, Yunhe, Rong Tang, and Chenchang Zhu. "The Controlling $$L_\infty $$-Algebra, Cohomology and Homotopy of Embedding Tensors and Lie–Leibniz Triples." Communications in Mathematical Physics 386, no. 1 (April 4, 2021): 269–304. http://dx.doi.org/10.1007/s00220-021-04032-y.

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AbstractIn this paper, we first construct the controlling algebras of embedding tensors and Lie–Leibniz triples, which turn out to be a graded Lie algebra and an $$L_\infty $$ L ∞ -algebra respectively. Then we introduce representations and cohomologies of embedding tensors and Lie–Leibniz triples, and show that there is a long exact sequence connecting various cohomologies. As applications, we classify infinitesimal deformations and central extensions using the second cohomology groups. Finally, we introduce the notion of a homotopy embedding tensor which will induce a Leibniz$$_\infty $$ ∞ -algebra. We realize Kotov and Strobl’s construction of an $$L_\infty $$ L ∞ -algebra from an embedding tensor, as a functor from the category of homotopy embedding tensors to that of Leibniz$$_\infty $$ ∞ -algebras, and a functor further to that of $$L_\infty $$ L ∞ -algebras.

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16

Hacque, Michel. "Cohomologies des anneaux-groupes." Communications in Algebra 18, no. 11 (January 1990): 3933–97. http://dx.doi.org/10.1080/00927879008824118.

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17

Inassaridze, H. "Non-Abelian Cohomology of Groups." gmj 4, no. 4 (August 1997): 313–31. http://dx.doi.org/10.1515/gmj.1997.313.

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Abstract Following Guin's approach to non-abelian cohomology [Guin, Pure Appl. Algebra 50: 109–137, 1988] and, using the notion of a crossed bimodule, a second pointed set of cohomology is defined with coefficients in a crossed module, and Guin's six-term exact cohomology sequence is extended to a nine-term exact sequence of cohomology up to dimension 2.

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18

Covez, Simon. "On the conjectural Leibniz cohomology for groups." Journal of K-theory 10, no. 3 (November 30, 2012): 519–63. http://dx.doi.org/10.1017/is011011011jkt195.

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AbstractThis article presents results which are consistent with conjectures about Leibniz (co)homology for discrete groups, due to J. L. Loday in 2003. We prove that rack cohomology has properties very close to the properties expected for the conjectural Leibniz cohomology. In particular, we prove the existence of a graded dendriform algebra structure on rack cohomology, and we construct a graded associative algebra morphism H•(−) → HR•(−) from group cohomology to rack cohomology which is injective for ● = 1.

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19

Lychagin, V., and L. Zil'bergleit. "Spencer cohomologies and symmetry groups." Acta Applicandae Mathematicae 41, no. 1-3 (December 1995): 227–45. http://dx.doi.org/10.1007/bf00996114.

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20

NG, CHI-KEUNG. "THE Ext-FUNCTOR OF COMPLETELY BOUNDED BI-COMODULES, INJECTIVITY AND COHOMOLOGY." International Journal of Mathematics 18, no. 07 (August 2007): 761–81. http://dx.doi.org/10.1142/s0129167x07004308.

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Suppose that S is a Hopf C*-algebra. Further to our study of the category of completely bounded S-comodules in [14], we will compare the Ext-functors for [Formula: see text] (the category of counital S-comodules) as well as for [Formula: see text] (the category of counital S-bicomodules) with the cohomology theories defined in [10]. The particular case of compact quantum groups as well as the cases of S=C0(G) and S = C*(G) (where G is a locally compact group) will be considered in more details. Moreover, we give some relations between the vanishing of the first dual cohomologies of C0(G) (respectively, C*(G)) and the injectivity of the bi-comodule U(G) (respectively, U(C*(G))).

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21

Iwase, Norio, and Akira Kono. "Adjoint action of a finite loop space. II." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 129, no. 4 (1999): 773–85. http://dx.doi.org/10.1017/s0308210500013135.

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Adjoint actions of compact simply connected Lie groups are studied by Kozima and the second author based on the series of studies on the classification of simple Lie groups and their cohomologies. At odd primes, the first author showed that there is a homotopy theoretic approach that will prove the results of Kozima and the second author for any 1-connected finite loop spaces. In this paper, we use the rationalization of the classifying space to compute the adjoint actions and the cohomology of classifying spaces assuming torsion free hypothesis, at the prime 2. And, by using Browder's work on the Kudo–Araki operations Q1 for homotopy commutative Hopf spaces, we show the converse for general 1-connected finite loop spaces, at the prime 2. This can be done because the inclusion j: G > BAG satisfies the homotopy commutativity for any non-homotopy commutative loop space G.

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22

Escudero, Juan García. "Randomness and Topological Invariants in Pentagonal Tiling Spaces." Discrete Dynamics in Nature and Society 2011 (2011): 1–23. http://dx.doi.org/10.1155/2011/946913.

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We analyze substitution tiling spaces with fivefold symmetry. In the substitution process, the introduction of randomness can be done by means of two methods which may be combined: composition of inflation rules for a given prototile set and tile rearrangements. The configurational entropy of the random substitution process is computed in the case of prototile subdivision followed by tile rearrangement. When aperiodic tilings are studied from the point of view of dynamical systems, rather than treating a single one, a collection of them is considered. Tiling spaces are defined for deterministic substitutions, which can be seen as the set of tilings that locally look like translates of a given tiling. Čech cohomology groups are the simplest topological invariants of such spaces. The cohomologies of two deterministic pentagonal tiling spaces are studied.

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23

KYED, DAVID, and HENRIK DENSING PETERSEN. "POLYNOMIAL COHOMOLOGY AND POLYNOMIAL MAPS ON NILPOTENT GROUPS." Glasgow Mathematical Journal 62, no. 3 (October 2, 2019): 706–36. http://dx.doi.org/10.1017/s0017089519000429.

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AbstractWe introduce a refined version of group cohomology and relate it to the space of polynomials on the group in question. We show that the polynomial cohomology with trivial coefficients admits a description in terms of ordinary cohomology with polynomial coefficients, and that the degree one polynomial cohomology with trivial coefficients admits a description directly in terms of polynomials. Lastly, we give a complete description of the polynomials on a connected, simply connected nilpotent Lie group by showing that these are exactly the maps that pull back to classical polynomials via the exponential map.

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24

Sambou, Salomon, and Mansour Sané. "Quelques résultats d'isomorphisme entre groupes de cohomologie." Annales Polonici Mathematici 104, no. 1 (2012): 97–103. http://dx.doi.org/10.4064/ap104-1-7.

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25

Barge, Jean. "Cohomologie des groupes et corps d'invariants multiplieatifs." Mathematische Annalen 283, no. 3 (September 1989): 519–28. http://dx.doi.org/10.1007/bf01442744.

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26

Guin, Daniel. "Cohomologie et homologie non abÉliennes des groupes." Journal of Pure and Applied Algebra 50, no. 2 (February 1988): 109–37. http://dx.doi.org/10.1016/0022-4049(88)90110-7.

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27

Heuer, Nicolaus. "Low-dimensional bounded cohomology and extensions of groups." MATHEMATICA SCANDINAVICA 126, no. 1 (March 29, 2020): 5–31. http://dx.doi.org/10.7146/math.scand.a-114969.

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Bounded cohomology of groups was first studied by Gromov in 1982 in his seminal paper M. Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. (1982), no. 56, 5–99. Since then it has sparked much research in Geometric Group Theory. However, it is notoriously hard to explicitly compute bounded cohomology, even for most basic “non-positively curved” groups. On the other hand, there is a well-known interpretation of ordinary group cohomology in dimension $2$ and $3$ in terms of group extensions. The aim of this paper is to make this interpretation available for bounded group cohomology. This will involve quasihomomorphisms as defined and studied by K. Fujiwara and M. Kapovich, On quasihomomorphisms with noncommutative targets, Geom. Funct. Anal. 26 (2016), no. 2, 478–519.

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28

Huber, Annette, Guido Kings, and Niko Naumann. "Some complements to the Lazard isomorphism." Compositio Mathematica 147, no. 1 (June 22, 2010): 235–62. http://dx.doi.org/10.1112/s0010437x10004884.

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AbstractLazard showed in his seminal work (Groupes analytiques p-adiques, Publ. Math. Inst. Hautes Études Sci. 26 (1965), 389–603) that for rational coefficients, continuous group cohomology of p-adic Lie groups is isomorphic to Lie algebra cohomology. We refine this result in two directions: first, we extend Lazard’s isomorphism to integral coefficients under certain conditions; and second, we show that for algebraic groups over finite extensions K/ℚp, his isomorphism can be generalized to K-analytic cochains andK-Lie algebra cohomology.

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29

Bertuccioni, Inta. "Brauer groups and cohomology." Archiv der Mathematik 84, no. 5 (May 2005): 406–11. http://dx.doi.org/10.1007/s00013-004-1202-0.

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30

Thomas, C. B. "COHOMOLOGY OF FINITE GROUPS." Bulletin of the London Mathematical Society 29, no. 1 (January 1997): 121–23. http://dx.doi.org/10.1112/blms/29.1.121.

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31

Salvetti, Mario. "Cohomology of Coxeter groups." Topology and its Applications 118, no. 1-2 (February 2002): 199–208. http://dx.doi.org/10.1016/s0166-8641(01)00051-7.

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32

Huebschmann, Johannes. "Cohomology of metacyclic groups." Transactions of the American Mathematical Society 328, no. 1 (January 1, 1991): 1–72. http://dx.doi.org/10.1090/s0002-9947-1991-1031239-1.

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33

Concini, C. de, and M. Salvetti. "Cohomology of Artin Groups." Mathematical Research Letters 3, no. 2 (1996): 293–97. http://dx.doi.org/10.4310/mrl.1996.v3.n2.a13.

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34

Hiller, Howard. "Cohomology of Bieberbach groups." Mathematika 32, no. 1 (June 1985): 55–59. http://dx.doi.org/10.1112/s002557930001086x.

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35

Pirashvili, Mariam. "Symmetric cohomology of groups." Journal of Algebra 509 (September 2018): 397–418. http://dx.doi.org/10.1016/j.jalgebra.2018.05.020.

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36

Dokuchaev, M., and M. Khrypchenko. "Partial cohomology of groups." Journal of Algebra 427 (April 2015): 142–82. http://dx.doi.org/10.1016/j.jalgebra.2014.11.030.

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37

Conduché, Daniel, Hvedri Inassaridze, and Nick Inassaridze. "Modq cohomology and Tate–Vogel cohomology of groups." Journal of Pure and Applied Algebra 189, no. 1-3 (May 2004): 61–87. http://dx.doi.org/10.1016/j.jpaa.2003.10.025.

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38

Baladze, V., and L. Turmanidze. "On Homology and Cohomology Groups of Remainders." gmj 11, no. 4 (December 2004): 613–33. http://dx.doi.org/10.1515/gmj.2004.613.

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Abstract Border homology and cohomology groups of pairs of uniform spaces are defined and studied. These groups give an intrinsic characterization of Čech type homology and cohomology groups of the remainder of a uniform space.

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39

Katok, Anatole, and Svetlana Katok. "Higher cohomology for Abelian groups of toral automorphisms." Ergodic Theory and Dynamical Systems 15, no. 3 (June 1995): 569–92. http://dx.doi.org/10.1017/s0143385700008531.

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AbstractWe give a complete description of smooth untwisted cohomology with coefficients in ℝl for ℤk-actions by hyperbolic automorphisms of a torus. For 1 ≤ n ≤ k − 1 the nth cohomology trivializes, i.e. every cocycle is cohomologous to a constant cocycle via a smooth coboundary. For n = k a counterpart of the classical Livshitz Theorem holds: the cohomology class of a smooth k-cocycle is determined by periodic data.

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40

Li, Jian-Shu, and Binyong Sun. "Low degree cohomologies of congruence groups." Science China Mathematics 62, no. 11 (February 21, 2019): 2287–308. http://dx.doi.org/10.1007/s11425-018-9476-8.

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41

Muranov, Yu V. "Tate cohomologies and Browder-Livesay groups of dihedral groups." Mathematical Notes 54, no. 2 (August 1993): 798–805. http://dx.doi.org/10.1007/bf01212844.

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42

Concini, C. de, and M. Salvetti. "Cohomology of Coxeter groups and Artin groups." Mathematical Research Letters 7, no. 2 (2000): 213–32. http://dx.doi.org/10.4310/mrl.2000.v7.n2.a7.

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43

Leary, I. J. "The integral cohomology rings of some p-groups." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 1 (July 1991): 25–32. http://dx.doi.org/10.1017/s0305004100070080.

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We determine the integral cohomology rings of an infinite family of p-groups, for odd primes p, with cyclic derived subgroups. Our method involves embedding the groups in a compact Lie group of dimension one, and was suggested independently by P. H. Kropholler and J. Huebschmann. This construction has also been used by the author to calculate the mod-p cohomology of the same groups and by B. Moselle to obtain partial results concerning the mod-p cohomology of the extra special p-groups [7], [9].

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44

Erovenko, Igor V. "On bounded cohomology of amalgamated products of groups." International Journal of Mathematics and Mathematical Sciences 2004, no. 40 (2004): 2103–21. http://dx.doi.org/10.1155/s0161171204311142.

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We investigate the structure of the singular part of the second bounded cohomology group of amalgamated products of groups by constructing an analog of the initial segment of the Mayer-Vietoris exact cohomology sequence for the spaces of pseudocharacters.

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45

Puls, Michael J. "Group Cohomology and Lp-Cohomology of Finitely Generated Groups." Canadian Mathematical Bulletin 46, no. 2 (June 1, 2003): 268–76. http://dx.doi.org/10.4153/cmb-2003-027-x.

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AbstractLet G be a finitely generated, infinite group, let p > 1, and let Lp(G) denote the Banach space . In this paper we will study the first cohomology group of G with coefficients in Lp(G), and the first reduced Lp-cohomology space of G. Most of our results will be for a class of groups that contains all finitely generated, infinite nilpotent groups.

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46

Magneron, Bernard. "Cohomologie des groupes et des espaces de transformation." Journal of Algebra 112, no. 2 (February 1988): 326–48. http://dx.doi.org/10.1016/0021-8693(88)90094-4.

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47

Barge, J. "Cohomologie des groupes et corps d'invariants multiplicatifs tordus." Commentarii Mathematici Helvetici 72, no. 1 (May 1997): 1–15. http://dx.doi.org/10.1007/pl00000360.

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48

Poonen, Bjorn, Damiano Testa, and Ronald van Luijk. "Computing Néron–Severi groups and cycle class groups." Compositio Mathematica 151, no. 4 (February 4, 2015): 713–34. http://dx.doi.org/10.1112/s0010437x14007878.

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Assuming the Tate conjecture and the computability of étale cohomology with finite coefficients, we give an algorithm that computes the Néron–Severi group of any smooth projective geometrically integral variety, and also the rank of the group of numerical equivalence classes of codimension $p$ cycles for any $p$.

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49

Chebolu, Sunil K., J. Daniel Christensen, and Ján Mináč. "Freyd's Generating Hypothesis for Groups with Periodic Cohomology." Canadian Mathematical Bulletin 55, no. 1 (March 1, 2012): 48–59. http://dx.doi.org/10.4153/cmb-2011-090-5.

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AbstractLet G be a finite group, and let k be a field whose characteristic p divides the order of G. Freyd's generating hypothesis for the stable module category of G is the statement that a map between finite-dimensional kG-modules in the thick subcategory generated by k factors through a projective if the induced map on Tate cohomology is trivial. We show that if G has periodic cohomology, then the generating hypothesis holds if and only if the Sylow p-subgroup of G is C2 or C3. We also give some other conditions that are equivalent to the GH for groups with periodic cohomology.

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50

Green, David John, and Pham Anh Minh. "Almost all extraspecial p-groups are swan groups." Bulletin of the Australian Mathematical Society 62, no. 1 (August 2000): 149–54. http://dx.doi.org/10.1017/s0004972700018566.

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Let P be an extraspecial p-group which is neither dihedral of order 8, nor of odd order p3 and exponent p. Let G be a finite group having P as a Sylow p-subgroup. Then the mod-p cohomology ring of G coincides with that of the normaliser NG (P).

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