Endomorphisms of Equivariant Algebraic $K$-theory
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916896752795648 |
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| author | Kumar, K. Arun Tripathi, Girja S |
| author_facet | Kumar, K. Arun Tripathi, Girja S |
| contents | We prove that for the action of a finite constant group scheme, equivariant algebraic $K$-theory is represented by a colimit of Grassmannians in the equivariant motivic homotopy category. Using this result we show that the set of endomorphisms of the equivariant motivic space defined by $K_0(G,-)$ coincides with the set of endomorphisms of infinite Grassmannians in the equivariant motivic homotopy category by explicitly computing the equivariant $K$-theory of Grassmannians. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_02544 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Endomorphisms of Equivariant Algebraic $K$-theory Kumar, K. Arun Tripathi, Girja S Algebraic Geometry Algebraic Topology K-Theory and Homology We prove that for the action of a finite constant group scheme, equivariant algebraic $K$-theory is represented by a colimit of Grassmannians in the equivariant motivic homotopy category. Using this result we show that the set of endomorphisms of the equivariant motivic space defined by $K_0(G,-)$ coincides with the set of endomorphisms of infinite Grassmannians in the equivariant motivic homotopy category by explicitly computing the equivariant $K$-theory of Grassmannians. |
| title | Endomorphisms of Equivariant Algebraic $K$-theory |
| topic | Algebraic Geometry Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2304.02544 |