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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2502.09462 |
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| _version_ | 1866915150479491072 |
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| author | Krishna, Amalendu Nath, Ritankar |
| author_facet | Krishna, Amalendu Nath, Ritankar |
| contents | We prove several completion theorems for equivariant K-theory
and cyclic homology of schemes with group action over a field. One of these
shows that for an algebraic space over a field acted upon by a linear algebraic
group, the derived completion of equivariant K'-theory at the
augmentation ideal of the representation ring of the group coincides with the
ordinary K'-theory of the bar construction associated to the group action.
This provides a solution to Thomason's completion problem. For action with finite
stabilizers, we show that the equivariant K-theory and cyclic homology have
non-equivariant descriptions even without passing to their completions. As an
application, we describe all equivariant Hochschild and
other homology groups for such actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09462 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thomason's completion for K-theory and cyclic homology of quotient stacks Krishna, Amalendu Nath, Ritankar Algebraic Geometry Primary 14F43, Secondary 19D55 We prove several completion theorems for equivariant K-theory and cyclic homology of schemes with group action over a field. One of these shows that for an algebraic space over a field acted upon by a linear algebraic group, the derived completion of equivariant K'-theory at the augmentation ideal of the representation ring of the group coincides with the ordinary K'-theory of the bar construction associated to the group action. This provides a solution to Thomason's completion problem. For action with finite stabilizers, we show that the equivariant K-theory and cyclic homology have non-equivariant descriptions even without passing to their completions. As an application, we describe all equivariant Hochschild and other homology groups for such actions. |
| title | Thomason's completion for K-theory and cyclic homology of quotient stacks |
| topic | Algebraic Geometry Primary 14F43, Secondary 19D55 |
| url | https://arxiv.org/abs/2502.09462 |