Grothendieck group of the stack of G-Zips
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2024
- DOI:
- 10.48550/arXiv.2410.01547
- arXiv:
- arXiv:2410.01547
- Bibcode:
- 2024arXiv241001547C
- Keywords:
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- Mathematics - Algebraic Geometry;
- 19A99 (primary);
- 14M15 (secondary)