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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2409.18925 |
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| _version_ | 1866917414501875712 |
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| author | Löwit, Jakub |
| author_facet | Löwit, Jakub |
| contents | We study torus-equivariant algebraic $K$-theory of affine Schubert varieties in the perfect affine Grassmannians over $\mathbb{F}_p$. We further compare it to the torus-equivariant Hochschild homology of perfect complexes, which has a geometric description in terms of global functions on certain fixed-point schemes. We prove that $\mathbb{F}_p$-linearly, this comparison is an isomorphism. Our approach is quite constructive, resulting in new computations of these $K$-theory rings. We establish various structural results for equivariant perfect algebraic $K$-theory on the way; we believe these are of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18925 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant $K$-theory, affine Grassmannian and perfection Löwit, Jakub Algebraic Geometry K-Theory and Homology We study torus-equivariant algebraic $K$-theory of affine Schubert varieties in the perfect affine Grassmannians over $\mathbb{F}_p$. We further compare it to the torus-equivariant Hochschild homology of perfect complexes, which has a geometric description in terms of global functions on certain fixed-point schemes. We prove that $\mathbb{F}_p$-linearly, this comparison is an isomorphism. Our approach is quite constructive, resulting in new computations of these $K$-theory rings. We establish various structural results for equivariant perfect algebraic $K$-theory on the way; we believe these are of independent interest. |
| title | Equivariant $K$-theory, affine Grassmannian and perfection |
| topic | Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2409.18925 |