Isotropic and numerical equivalence for Chow groups and Morava K-theories
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910545072881664 |
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| author | Vishik, Alexander |
| author_facet | Vishik, Alexander |
| contents | In this paper we prove the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with ${\Bbb{F}}_p$-coefficients). This shows that Isotropic Chow motives coincide with Numerical Chow motives. In particular, homs between such objects are finite groups and $\otimes$ has no zero-divisors. It provides a large supply of new points for the Balmer spectrum of the Voevodsky motivic category. We also prove the Morava K-theory version of the above result, which permits to construct plenty of new points for the Balmer spectrum of the Morel-Voevodsky ${\Bbb{A}}^1$-stable homotopic category. This substantially improves our understanding of the mentioned spectra whose description is a major open problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_15148 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Isotropic and numerical equivalence for Chow groups and Morava K-theories Vishik, Alexander Algebraic Geometry Algebraic Topology K-Theory and Homology 14C15, 14C25, 19E15, 14F42 In this paper we prove the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with ${\Bbb{F}}_p$-coefficients). This shows that Isotropic Chow motives coincide with Numerical Chow motives. In particular, homs between such objects are finite groups and $\otimes$ has no zero-divisors. It provides a large supply of new points for the Balmer spectrum of the Voevodsky motivic category. We also prove the Morava K-theory version of the above result, which permits to construct plenty of new points for the Balmer spectrum of the Morel-Voevodsky ${\Bbb{A}}^1$-stable homotopic category. This substantially improves our understanding of the mentioned spectra whose description is a major open problem. |
| title | Isotropic and numerical equivalence for Chow groups and Morava K-theories |
| topic | Algebraic Geometry Algebraic Topology K-Theory and Homology 14C15, 14C25, 19E15, 14F42 |
| url | https://arxiv.org/abs/2307.15148 |