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

Author:

Alexander Vishik

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Algebraic Topology (math.AT), K-Theory and Homology (math.KT)

journal:

date:

2023-07-26 16:00:00

Abstract

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.

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