ALEXANDER VISHIK ALEXANDER.VISHIK@NOTTINGHAM.AC.UK
Professor of Algebra
Isotropic and numerical equivalence for Chow groups and Morava K-theories
Vishik, Alexander
Authors
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, https://doi.org/10.1007/s00222-024-01267-z
Journal Article Type | Article |
---|---|
Acceptance Date | May 3, 2024 |
Online Publication Date | May 27, 2024 |
Publication Date | 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 |
DOI | https://doi.org/10.1007/s00222-024-01267-z |
Public URL | https://nottingham-repository.worktribe.com/output/34632421 |
Publisher URL | https://link.springer.com/article/10.1007/s00222-024-01267-z |
Files
s00222-024-01267-z
(1.4 Mb)
PDF
Publisher Licence URL
https://creativecommons.org/licenses/by/4.0/
You might also like
On isotropic and numerical equivalence of cycles
(2022)
Journal Article
ISOTROPIC MOTIVES
(2020)
Journal Article
Operations and poly-operations in algebraic cobordism
(2020)
Journal Article
Affine quadrics and the Picard group of the motivic category
(2019)
Journal Article
Stable and unstable operations in algebraic cobordism
(2019)
Journal Article
Downloadable Citations
About Repository@Nottingham
Administrator e-mail: discovery-access-systems@nottingham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search