6 papers · 1 filter
Semiinfinite sheaves on affine flag varieties
Pramod N. Achar, Gurbir Dhillon, Simon Riche
We study a category of semiinfinite sheaves on the affine flag variety of a connected reductive algebraic group, with coefficients in a field (of arbitrary characteristic different…
Equivariant Koszul Duality, Modular Category , and Periodic Kazhdan--Lusztig Polynomials
Simon Riche, Quan Situ
Let be a connected reductive algebraic group over an algebraically closed field of positive characteristic, be its Lie algebra, and be a Borel subgroup. We p…
Tilting modules for reductive algebraic groups: characters and support varieties
Pramod N. Achar, Simon Riche
These notes are our contribution to the Proceedings of the ICM 2026. We discuss some results we have obtained (in part jointly with coauthors) regarding the representation theory o…
Mixed modular perverse sheaves on affine flag varieties and Koszul duality
Simon Riche
Under some technical assumptions, and building on joint work with Bezrukavnikov, we prove a multiplicity formula for indecomposable tilting perverse sheaves on affine flag varietie…
On the modular generalized Springer correspondence for disconnected groups
Kostas I. Psaromiligkos, Simon Riche
We study the construction of a modular generalized Springer correspondence for a possibly disconnected complex reductive algebraic group.
Modular intersection cohomology of Drinfeld's compactifications
Pramod N. Achar, Gurbir Dhillon, Simon Riche
We compute the dimension of the cohomology of stalks of intersection cohomology complexes on Zastava schemes and Drinfeld compactifications associated with a connected reductive al…