On isotropic and numerical equivalence of cycles

Vishik, Alexander

Abstract

We study the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with Fp-coefficients). This conjecture is essential for understanding the structure of the isotropic motivic category and that of the tensor triangulated spectrum of Voevodsky category of motives. We prove the conjecture for the new range of cases. In particular, we show that, for a given variety X, it holds for sufficiently large primes p. We also prove the p-adic analogue. This permits to interpret integral numerically trivial classes in CH (X) as p∞-anisotropic ones.

Citation

Vishik, A. (2022). On isotropic and numerical equivalence of cycles. Selecta Mathematica (New Series), 29(1), Article 8. https://doi.org/10.1007/s00029-022-00812-z

• Journal Article Type: Article
• Acceptance Date: Sep 27, 2022
• Online Publication Date: Nov 12, 2022
• Publication Date: Nov 12, 2022
• Deposit Date: Sep 29, 2022
• Publicly Available Date: Nov 13, 2023
• Journal: Selecta Mathematica, New Series
• Print ISSN: 1022-1824
• Electronic ISSN: 1420-9020
• Peer Reviewed: Peer Reviewed
• Volume: 29
• Issue: 1
• Article Number: 8
• DOI: https://doi.org/10.1007/s00029-022-00812-z
• Public URL: https://nottingham-repository.worktribe.com/output/11753847
• Publisher URL: https://link.springer.com/article/10.1007/s00029-022-00812-z