Categorical Milnor squares and K-theory of algebraic stacks
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866913510533890048 |
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| author | Bachmann, Tom Khan, Adeel A. Ravi, Charanya Sosnilo, Vladimir |
| author_facet | Bachmann, Tom Khan, Adeel A. Ravi, Charanya Sosnilo, Vladimir |
| contents | We introduce a notion of Milnor square of stable $\infty$-categories and prove a criterion under which algebraic K-theory sends such a square to a cartesian square of spectra. We apply this to prove Milnor excision and proper excision theorems in the K-theory of algebraic stacks with affine diagonal and nice stabilizers. This yields a generalization of Weibel's conjecture on the vanishing of negative K-groups for this class of stacks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_04355 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Categorical Milnor squares and K-theory of algebraic stacks Bachmann, Tom Khan, Adeel A. Ravi, Charanya Sosnilo, Vladimir Algebraic Geometry K-Theory and Homology 14F08, 19E08, 19D35, 14D23 We introduce a notion of Milnor square of stable $\infty$-categories and prove a criterion under which algebraic K-theory sends such a square to a cartesian square of spectra. We apply this to prove Milnor excision and proper excision theorems in the K-theory of algebraic stacks with affine diagonal and nice stabilizers. This yields a generalization of Weibel's conjecture on the vanishing of negative K-groups for this class of stacks. |
| title | Categorical Milnor squares and K-theory of algebraic stacks |
| topic | Algebraic Geometry K-Theory and Homology 14F08, 19E08, 19D35, 14D23 |
| url | https://arxiv.org/abs/2011.04355 |