Relevant bibliographies by topics / Microlocal sheaves

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Academic literature on the topic 'Microlocal sheaves'

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

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Journal articles on the topic "Microlocal sheaves"

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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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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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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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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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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Books on the topic "Microlocal sheaves"

1

Kashiwara, Masaki. Microlocal study of sheaves. Société Mathématique de France, 1985.

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2

1943-, Schapira Pierre, and Société mathématique de France, eds. Microlocal study of sheaves. Société mathématique de France, 1985.

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Kashiwara, Masaki. Microlocal study of sheaves. Société mathématique de France, 1985.

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Kashiwara, Masaki. Microlocal study of sheaves. Société mathématique de France, 1985.

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5

Getmanenko, Alexander. Microlocal properties of sheaves and complex WKB. Société mathématique de France, 2013.

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6

1943-, Schapira Pierre, ed. Micrological study of sheaves. Société mathématique de France, 1985.

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7

Cunningham, Clifton, Andrew Fiori, James Mracek, Bin Xu, and Ahmed Moussaoui. Arthur Packets for $p$-Adic Groups by Way of Microlocal Vanishing Cycles of Perverse Sheaves, with Examples. American Mathematical Society, 2022.

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Book chapters on the topic "Microlocal sheaves"

1

Adams, Jeffrey, Dan Barbasch, and David A. Vogan. "Microlocal geometry of perverse sheaves." In The Langlands Classification and Irreducible Characters for Reductive Groups. Birkhäuser Boston, 1992. http://dx.doi.org/10.1007/978-1-4612-0383-4_24.

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2

Schapira, Pierre. "Study of Sheaves of Solutions of Microdifferential Systems." In Advances in Microlocal Analysis. Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4606-4_11.

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Guillermou, Stéphane, and Pierre Schapira. "Microlocal Theory of Sheaves and Tamarkin’s Non Displaceability Theorem." In Lecture Notes of the Unione Matematica Italiana. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06514-4_3.

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