A geometric model for blocks of Frobenius kernels - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2022

A geometric model for blocks of Frobenius kernels

Abstract

Building on a geometric counterpart of Steinberg's tensor product formula for simple representations of a connected reductive algebraic group G over a field of positive characteristic, and following an idea of Arkhipov--Bezrukavnikov--Braverman--Gaitsgory--Mirkovic, we define and initiate the study of some categories of perverse sheaves on the affine Grassmannian of the Langlands dual group to G that should provide geometric models for blocks of representations of the Frobenius kernel G_1 of G. In particular, we show that these categories admit enough projective and injective objects, which are closely related to some tilting perverse sheaves, and that they are highest weight categories in an appropriate generalized sense.
Fichier principal
Vignette du fichier
Rmod-new.pdf (826.21 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03602356 , version 1 (09-03-2022)

Identifiers

Cite

Pramod Achar, Simon Riche. A geometric model for blocks of Frobenius kernels. 2022. ⟨hal-03602356⟩
29 View
28 Download

Altmetric

Share

Gmail Facebook X LinkedIn More