Lambda-ring structures on the K-theory of algebraic stacks
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913430656516096 |
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| author | Joshua, Roy Pelaez, Pablo |
| author_facet | Joshua, Roy Pelaez, Pablo |
| contents | In this paper we consider the K-theory of smooth algebraic stacks, establish lambda and gamma operations, and show that the higher K-theory of such stacks is always a pre-lambda-ring, and is a lambda-ring if every coherent sheaf is the quotient of a vector bundle. As a consequence, we are able to define Adams operations and absolute cohomology for smooth algebraic stacks satisfying this hypothesis. We also obtain a comparison of the absolute cohomology with the equivariant higher Chow groups in certain special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10394 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lambda-ring structures on the K-theory of algebraic stacks Joshua, Roy Pelaez, Pablo K-Theory and Homology 19E08, 14D23, 14L30 In this paper we consider the K-theory of smooth algebraic stacks, establish lambda and gamma operations, and show that the higher K-theory of such stacks is always a pre-lambda-ring, and is a lambda-ring if every coherent sheaf is the quotient of a vector bundle. As a consequence, we are able to define Adams operations and absolute cohomology for smooth algebraic stacks satisfying this hypothesis. We also obtain a comparison of the absolute cohomology with the equivariant higher Chow groups in certain special cases. |
| title | Lambda-ring structures on the K-theory of algebraic stacks |
| topic | K-Theory and Homology 19E08, 14D23, 14L30 |
| url | https://arxiv.org/abs/2407.10394 |