Some remarks on Chow correspondences

TL;DR

This paper explores various equivalence relations on Chow rings within Voevodsky's triangulated category of motives, providing insights into their properties and interrelations.

Contribution

It introduces and analyzes several adequate equivalence relations on Chow rings in the context of Voevodsky's motives, advancing understanding of their structure.

Findings

Identifies and compares different equivalence relations on Chow rings.

Provides conditions under which these equivalence relations coincide or differ.

Enhances the theoretical framework of motives and Chow rings.

Abstract

We study, in the context of Voevodsky's triangulated category of motives, several adequate equivalence relations (in the sense of Samuel) on the graded Chow ring $CH^\ast (X\times Y)$ for $X$, $Y$ smooth projective varieties over a field.