Isotropic and numerical equivalence for Chow groups and Morava K-theories

Vishik, Alexander

Abstract

In this paper we prove the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with Fp-coefficients). This shows that Isotropic Chow motives coincide with Numerical Chow motives. In particular, homs between such objects are finite groups and ⊗ 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 A1-stable homotopy category. This substantially improves our understanding of the mentioned spectra whose description is a major open problem.

Citation

Vishik, A. (2024). Isotropic and numerical equivalence for Chow groups and Morava K-theories. Inventiones Mathematicae, 237(2), 779-808. https://doi.org/10.1007/s00222-024-01267-z

• Journal Article Type: Article
• Acceptance Date: May 10, 2024
• Online Publication Date: May 27, 2024
• Publication Date: May 27, 2024
• Deposit Date: May 10, 2024
• Publicly Available Date: May 25, 2025
• Journal: Inventiones Mathematicae
• Print ISSN: 0020-9910
• Electronic ISSN: 1432-1297
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 237
• Issue: 2
• Pages: 779-808
• DOI: https://doi.org/10.1007/s00222-024-01267-z
• Keywords: 14F42, 14C25, 19E15, 14C15
• Public URL: https://nottingham-repository.worktribe.com/output/34632421
• Publisher URL: https://link.springer.com/article/10.1007/s00222-024-01267-z
• Additional Information: Received: 28 July 2023; Accepted: 10 May 2024; First Online: 27 May 2024