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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2505.12357 |
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| _version_ | 1866910972371795968 |
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| author | Sala, Francesco Schadeck, Laurent Vistoli, Angelo |
| author_facet | Sala, Francesco Schadeck, Laurent Vistoli, Angelo |
| contents | Given a quotient of a regular noetherian separated algebraic space $X$ over a field by an affine algebraic group $G$ having finite stabilizers (with some mild technical conditions), G. Vezzosi and A. Vistoli defined the geometric part of the rational equivariant K-theory $K(X,G)$ and conjectured that it is isomorphic to the rational K-theory of the quotient $X/G$. In this paper we refine the construction of geometric K-theory to the rational K-theory of a quotient stack $[X/G]$ over an arbitrary excellent base; we show that it is part of an intrinsic decomposition of the K-theory of the stack and prove many properties that make it amenable to computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12357 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The geometric K-theory of quotient stacks Sala, Francesco Schadeck, Laurent Vistoli, Angelo Algebraic Geometry Given a quotient of a regular noetherian separated algebraic space $X$ over a field by an affine algebraic group $G$ having finite stabilizers (with some mild technical conditions), G. Vezzosi and A. Vistoli defined the geometric part of the rational equivariant K-theory $K(X,G)$ and conjectured that it is isomorphic to the rational K-theory of the quotient $X/G$. In this paper we refine the construction of geometric K-theory to the rational K-theory of a quotient stack $[X/G]$ over an arbitrary excellent base; we show that it is part of an intrinsic decomposition of the K-theory of the stack and prove many properties that make it amenable to computations. |
| title | The geometric K-theory of quotient stacks |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2505.12357 |