Decomposition numbers for perverse sheaves

Daniel Juteau[1]

  • [1] Mathematical Sciences Research Institute 17 Gauss Way Berkeley, CA 94720 (USA)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 3, page 1177-1229
  • ISSN: 0373-0956

Abstract

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The purpose of this article is to set foundations for decomposition numbers of perverse sheaves, to give some methods to calculate them in simple cases, and to compute them concretely in two situations: for a simple (Kleinian) surface singularity, and for the closure of the minimal non-trivial nilpotent orbit in a simple Lie algebra.This work has applications to modular representation theory, for Weyl groups using the nilpotent cone of the corresponding semisimple Lie algebra, and for reductive algebraic group schemes using the affine Grassmannian of the Langlands dual group.

How to cite

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Juteau, Daniel. "Decomposition numbers for perverse sheaves." Annales de l’institut Fourier 59.3 (2009): 1177-1229. <http://eudml.org/doc/10420>.

@article{Juteau2009,
abstract = {The purpose of this article is to set foundations for decomposition numbers of perverse sheaves, to give some methods to calculate them in simple cases, and to compute them concretely in two situations: for a simple (Kleinian) surface singularity, and for the closure of the minimal non-trivial nilpotent orbit in a simple Lie algebra.This work has applications to modular representation theory, for Weyl groups using the nilpotent cone of the corresponding semisimple Lie algebra, and for reductive algebraic group schemes using the affine Grassmannian of the Langlands dual group.},
affiliation = {Mathematical Sciences Research Institute 17 Gauss Way Berkeley, CA 94720 (USA)},
author = {Juteau, Daniel},
journal = {Annales de l’institut Fourier},
keywords = {Perverse sheaves; intersection cohomology; integral cohomology; t-structures; torsion theories; decomposition matrices; simple singularities; minimal nilpotent orbits; perverse sheaves; -structures},
language = {eng},
number = {3},
pages = {1177-1229},
publisher = {Association des Annales de l’institut Fourier},
title = {Decomposition numbers for perverse sheaves},
url = {http://eudml.org/doc/10420},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Juteau, Daniel
TI - Decomposition numbers for perverse sheaves
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 3
SP - 1177
EP - 1229
AB - The purpose of this article is to set foundations for decomposition numbers of perverse sheaves, to give some methods to calculate them in simple cases, and to compute them concretely in two situations: for a simple (Kleinian) surface singularity, and for the closure of the minimal non-trivial nilpotent orbit in a simple Lie algebra.This work has applications to modular representation theory, for Weyl groups using the nilpotent cone of the corresponding semisimple Lie algebra, and for reductive algebraic group schemes using the affine Grassmannian of the Langlands dual group.
LA - eng
KW - Perverse sheaves; intersection cohomology; integral cohomology; t-structures; torsion theories; decomposition matrices; simple singularities; minimal nilpotent orbits; perverse sheaves; -structures
UR - http://eudml.org/doc/10420
ER -

References

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