6 papers
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…
Steinberg quotients and Smith-Treumann localization
Pramod N. Achar, Paul Sobaje
Smith-Treumann localization for sheaves on the affine Grassmannian of a reductive group has previously been studied by Leslie-Lonergan (for spherical sheaves) and by Riche-Williams…
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…
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…
Equivariant sheaves for classical groups acting on Grassmannians
Pramod N. Achar, Tamanna Chatterjee
Let be a finite-dimensional complex vector space. Assume that is a direct sum of subspaces each of which is equipped with a nondegenerate symmetric or skew-symmetric biline…
On global Schubert varieties for the general linear group
Pramod N. Achar, Andrea Bourque
We give a "lattice-theoretic" description of the global Schubert variety for associated to any dominant coweight.