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Journal articles on the topic 'Microlocal sheaves'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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1

Nadler, David. "Microlocal branes are constructible sheaves." Selecta Mathematica 15, no. 4 (2009): 563–619. http://dx.doi.org/10.1007/s00029-009-0008-0.

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2

Bezrukavnikov, Roman, and Mikhail Kapranov. "Microlocal sheaves and quiver varieties." Annales de la faculté des sciences de Toulouse Mathématiques 25, no. 2-3 (2016): 473–516. http://dx.doi.org/10.5802/afst.1502.

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3

Braden, Tom. "Perverse Sheaves on Grassmannians." Canadian Journal of Mathematics 54, no. 3 (2002): 493–532. http://dx.doi.org/10.4153/cjm-2002-017-6.

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AbstractWe compute the category of perverse sheaves on Hermitian symmetric spaces in types A and D, constructible with respect to the Schubert stratification. The calculation is microlocal, and uses the action of the Borel group to study the geometry of the conormal variety Λ.
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4

Waschkies, Ingo. "The stack of microlocal perverse sheaves." Bulletin de la Société mathématique de France 132, no. 3 (2004): 397–462. http://dx.doi.org/10.24033/bsmf.2469.

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5

Koppensteiner, Clemens. "Exact functors on perverse coherent sheaves." Compositio Mathematica 151, no. 9 (2015): 1688–96. http://dx.doi.org/10.1112/s0010437x15007265.

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Inspired by symplectic geometry and a microlocal characterizations of perverse (constructible) sheaves we consider an alternative definition of perverse coherent sheaves. We show that a coherent sheaf is perverse if and only if $R{\rm\Gamma}_{Z}{\mathcal{F}}$ is concentrated in degree $0$ for special subvarieties $Z$ of $X$. These subvarieties $Z$ are analogs of Lagrangians in the symplectic case.
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6

D'Agnolo, Andrea. "On the microlocal cut-off of sheaves." Topological Methods in Nonlinear Analysis 8, no. 1 (1996): 161. http://dx.doi.org/10.12775/tmna.1996.025.

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7

Kashiwara, Masaki, and Pierre Schapira. "Microlocal Euler classes and Hochschild homology." Journal of the Institute of Mathematics of Jussieu 13, no. 3 (2013): 487–516. http://dx.doi.org/10.1017/s1474748013000169.

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AbstractWe define the notion of a trace kernel on a manifold $M$. Roughly speaking, it is a sheaf on $M\times M$ for which the formalism of Hochschild homology applies. We associate a microlocal Euler class with such a kernel, a cohomology class with values in the relative dualizing complex of the cotangent bundle ${T}^{\ast } M$ over $M$, and we prove that this class is functorial with respect to the composition of kernels.This generalizes, unifies and simplifies various results from (relative) index theorems for constructible sheaves, $\mathscr{D}$-modules and elliptic pairs.
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8

Hennecart, Lucien. "Microlocal characterization of Lusztig sheaves for affine quivers and 𝑔-loops quivers". Representation Theory of the American Mathematical Society 26, № 2 (2022): 17–67. http://dx.doi.org/10.1090/ert/595.

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We prove that for extended Dynkin quivers, simple perverse sheaves in Lusztig category are characterized by the nilpotency of their singular support. This proves a conjecture of Lusztig in the case of affine quivers. For cyclic quivers, we prove a similar result for a larger nilpotent variety and a larger class of perverse sheaves. We formulate conjectures concerning similar results for quivers with loops, for which we have to use the appropriate notion of nilpotent variety, due to Bozec, Schiffmann and Vasserot. We prove our conjecture for g g -loops quivers ( g ≥ 2 g\geq 2 ).
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9

Tose, Nobuyuki. "Systems of microdifferential equations with involutory double characteristics propagation theorem for sheaves in the frameworkof microlocal study of sheaves." Proceedings of the Japan Academy, Series A, Mathematical Sciences 63, no. 7 (1987): 262–65. http://dx.doi.org/10.3792/pjaa.63.262.

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10

d'Agnolo, Andrea, and Giuseppe Zampieri. "Microlocal direct images of simple sheaves with applications to systems with simple characteristics." Bulletin de la Société mathématique de France 123, no. 4 (1995): 605–37. http://dx.doi.org/10.24033/bsmf.2273.

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11

Jin, Xin. "A Hamiltonian ∐ n BO(n)-action, stratified Morse theory and the J-homomorphism." Compositio Mathematica 160, no. 9 (2024): 2005–99. http://dx.doi.org/10.1112/s0010437x24007279.

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We use sheaves of spectra to quantize a Hamiltonian $\coprod _n BO(n)$ -action on $\varinjlim _{N}T^*\mathbf {R}^N$ that naturally arises from Bott periodicity. We employ the category of correspondences developed by Gaitsgory and Rozenblyum [A study in derived algebraic geometry, vol. I. Correspondences and duality, Mathematical Surveys and Monographs, vol. 221 (American Mathematical Society, 2017)] to give an enrichment of stratified Morse theory by the $J$ -homomorphism. This provides a key step in the work of Jin [Microlocal sheaf categories and the $J$ -homomorphism, Preprint (2020), arXiv
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12

Zhang, Bingyu. "Non-linear microlocal cut-off functors." Rendiconti del Seminario Matematico della Università di Padova, January 13, 2025. https://doi.org/10.4171/rsmup/174.

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To any conic closed set of a cotangent bundle, one can associate four functors on the category of sheaves, which are called non-linear microlocal cut-off functors. Here we explain their relation with the microlocal cut-off functor defined by Kashiwara and Schapira, and prove a microlocal cut-off lemma for non-linear microlocal cut-off functors, adapting inputs from symplectic geometry. We also prove two Künneth formulas and a functor classification result for categories of sheaves with microsupport conditions.
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13

Kashiwara, Masaki, and Pierre Schapira. "Piecewise Linear Sheaves." International Mathematics Research Notices, August 2, 2019. http://dx.doi.org/10.1093/imrn/rnz145.

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Abstract On a finite-dimensional real vector space, we give a microlocal characterization of (derived) piecewise linear sheaves (PL sheaves) and prove that the triangulated category of such sheaves is generated by sheaves associated with convex polyhedra. We then give a similar theorem for PL $\gamma $-sheaves, that is, PL sheaves associated with the $\gamma $-topology, for a closed convex polyhedral proper cone $\gamma $. Our motivation is that convex polyhedra may be considered as building blocks for higher dimensional barcodes.
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14

Kuo, Christopher, and Wenyuan Li. "Duality and Kernels in Microlocal Geometry." International Mathematics Research Notices 2025, no. 6 (2025). https://doi.org/10.1093/imrn/rnaf070.

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Abstract We study the dualizability of sheaves on manifolds with isotropic singular supports $\operatorname{Sh}_\Lambda (M)$ and microsheaves with isotropic supports $\operatorname{\mu sh}_\Lambda (\Lambda )$ and obtain a classification result of colimit-preserving functors by convolutions of sheaf kernels. Moreover, for sheaves with isotropic singular supports and compact supports $\operatorname{Sh}_\Lambda ^{b}(M)_{0}$, the standard categorical duality and Verdier duality are related by the wrap-once functor, which is the inverse Serre functor in proper objects, and we thus show that the Ver
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15

GETMANENKO, Alexander, and Dmitry TAMARKIN. "Microlocal properties of sheaves and complex WKB." Astérisque, November 6, 2018. http://dx.doi.org/10.24033/ast.926.

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16

Jin, Xin, and David Treumann. "Brane structures in microlocal sheaf theory." Journal of Topology 17, no. 1 (2024). http://dx.doi.org/10.1112/topo.12325.

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AbstractLet be an exact Lagrangian submanifold of a cotangent bundle , asymptotic to a Legendrian submanifold . We study a locally constant sheaf of ‐categories on , called the sheaf of brane structures or . Its fiber is the ‐category of spectra, and we construct a Hamiltonian invariant, fully faithful functor from to the ‐category of sheaves of spectra on with singular support in .
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17

Cunningham, Clifton, and Mishty Ray. "Proof of Vogan’s conjecture on Arthur packets: irreducible parameters of p-adic general linear groups." manuscripta mathematica, July 14, 2023. http://dx.doi.org/10.1007/s00229-023-01490-7.

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AbstractIn this paper we prove Vogan’s conjecture on local Arthur packets, as recalled in Cunningham et al. [Arthur packets for p-adic groups by way of microlocal vanishing cycles of perverse sheaves, with examples, Memoirs of the American Mathematical Society, Boston, 2022, Section 8.3, Conjecture 1(a)], for irreducible Arthur parameters of p-adic general linear groups. This result shows that these Arthur packets may be characterized by properties of simple perverse sheaves on a moduli space of Langlands parameters.
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18

Asano, Tomohiro, Yuichi Ike, and Wenyuan Li. "Lagrangian cobordism and shadow distance in Tamarkin category." Selecta Mathematica 31, no. 3 (2025). https://doi.org/10.1007/s00029-025-01034-9.

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Abstract We study exact Lagrangian cobordisms between exact Lagrangians in a cotangent bundle in the sense of Arnol’d, using microlocal theory of sheaves. We construct a sheaf quantization for an exact Lagrangian cobordism between Lagrangians with conical ends, prove an iterated cone decomposition of the sheaf quantization for cobordisms with multiple ends, and show that the interleaving distance of sheaves is bounded by the shadow distance of the cobordism. Using the result, we prove a rigidity result on Lagrangian intersection by estimating the energy cost of splitting and connecting Lagrang
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19

Færgeman, Joakim, and Sam Raskin. "Non-vanishing of geometric Whittaker coefficients for reductive groups." Journal of the American Mathematical Society, April 25, 2025. https://doi.org/10.1090/jams/1051.

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We prove that cuspidal automorphic D D -modules have non-vanishing Whittaker coefficients, generalizing known results in the geometric Langlands program from G L n GL_n to general reductive groups. The key tool is a microlocal interpretation of Whittaker coefficients. We establish various exactness properties in the geometric Langlands context that may be of independent interest. Specifically, we show Hecke functors are t t -exact on the category of tempered D D -modules, strengthening a classical result of Gaitsgory (with different hypotheses) for G L n GL_n . We also show that Whittaker coef
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20

Cunningham, Clifton, Andrew Fiori, Ahmed Moussaoui, James Mracek та Bin Xu. "Arthur packets for 𝑝-adic groups by way of microlocal vanishing cycles of perverse sheaves, with examples". Memoirs of the American Mathematical Society 276, № 1353 (2022). http://dx.doi.org/10.1090/memo/1353.

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In this article we propose a geometric description of Arthur packets for p p -adic groups using vanishing cycles of perverse sheaves. Our approach is inspired by the 1992 book by Adams, Barbasch and Vogan on the Langlands classification of admissible representations of real groups and follows the direction indicated by Vogan in his 1993 paper on the Langlands correspondence. Using vanishing cycles, we introduce and study a functor from the category of equivariant perverse sheaves on the moduli space of certain Langlands parameters to local systems on the regular part of the conormal bundle for
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21

Shen, Linhui, and Daping Weng. "Cluster Structures on Double Bott–Samelson Cells." Forum of Mathematics, Sigma 9 (2021). http://dx.doi.org/10.1017/fms.2021.59.

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Abstract Let $\mathsf {C}$ be a symmetrisable generalised Cartan matrix. We introduce four different versions of double Bott–Samelson cells for every pair of positive braids in the generalised braid group associated to $\mathsf {C}$ . We prove that the decorated double Bott–Samelson cells are smooth affine varieties, whose coordinate rings are naturally isomorphic to upper cluster algebras. We explicitly describe the Donaldson–Thomas transformations on double Bott–Samelson cells and prove that they are cluster transformations. As an application, we complete the proof of the Fock–Goncharov dual
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22

Emmerson, Parker Yaohushuason. "Foundations of Categorical-Homotopical Operator Algebras, Daisy Network Dynamics, and Anterolateral Spectral Algebra." Journal of Liberated Mathematics, May 25, 2025. https://doi.org/10.5281/zenodo.15509974.

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This paper introduces and formalizes six novel mathematical frameworks synthesizing categorical, homotopical, operator-algebraic, and spectral constructs with emergent symmetry and criticality. We define \emph{ultranaut operators} as higher-categorical homotopy-enriched transitions; construct spectral decompositions over $\Sigma$-enriched matrices; develop integral operator algebra formalism; introduce the \emph{daisy network}, a self-similar symmetry-generating topological graph; analyze paradoxical scale-interaction criticality ($1 \ll Q \ll 1$); and establish \emph{anterolateral spectral al
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