Grothendieck group of the stack of G-Zips
Algebraic Geometry
2024-10-03 v1
Abstract
Given a connected reductive group G over the finite field of order p and a cocharacter of G over the algebraic closure of the finite field, we can define G-Zips. The collection of these G-Zips form an algebraic stack which is a stack quotient of G. In this paper we study the K-theory rings of this quotient stack, focusing on the Grothendieck group. Under the additional assumption that the derived group is simply connected, the Grothendieck group is described as a quotient of the representation ring of the Levi subgroup centralising the cocharacter.
Keywords
Cite
@article{arxiv.2410.01547,
title = {Grothendieck group of the stack of G-Zips},
author = {Simon Cooper},
journal= {arXiv preprint arXiv:2410.01547},
year = {2024}
}