Decomposition numbers for perverse sheaves

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 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.

References in corpus (1)

• Cohomology of the minimal nilpotent orbit

Cited by in corpus (15)

• Parity Sheaves
• Modular Koszul duality
• Modular perverse sheaves on flag varieties II: Koszul duality and formality
• Weyl group actions on the Springer sheaf
• Cohomology of the minimal nilpotent orbit
• Regular holonomic D[[h]]-modules
• Modular representations of reductive groups and geometry of affine Grassmannians
• Perverse sheaves and modular representation theory
• Modular generalized Springer correspondence II: classical groups
• Congruences automorphes et torsion dans la cohomologie d'un système local d'Harris-Taylor
• Modular Springer correspondence, decomposition matrices and basic sets
• Kumar's criterion modulo p
• Cohomology with integral coefficients of stacks of shtukas
• Torsion Pairs in Recollements of Abelian Categories
• Sur les extensions intermédiaires des systèmes locaux d'Harris-Taylor