Grothendieck group of the stack of G-Zips
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909333072117760 |
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| author | Cooper, Simon |
| author_facet | Cooper, Simon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01547 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Grothendieck group of the stack of G-Zips Cooper, Simon Algebraic Geometry 19A99 (primary), 14M15 (secondary) 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. |
| title | Grothendieck group of the stack of G-Zips |
| topic | Algebraic Geometry 19A99 (primary), 14M15 (secondary) |
| url | https://arxiv.org/abs/2410.01547 |