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On isotropic and numerical equivalence of cycles

Vishik, Alexander



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.


Vishik, A. (2022). On isotropic and numerical equivalence of cycles. Selecta Mathematica (New Series), 29(1), Article 8.

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
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 29
Issue 1
Article Number 8
Public URL
Publisher URL


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