A short note on the weak Lefschetz property for Chow groups

TL;DR

This paper explores a covariant weak Lefschetz property for Chow groups inspired by the Bloch-Beilinson conjectures, proving it in specific cases using Kimura's nilpotence theorem.

Contribution

It introduces a new covariant weak Lefschetz property for Chow groups and proves it in certain cases, advancing understanding of algebraic cycles.

Findings

Proves the covariant weak Lefschetz property in some special cases

Uses Kimura's nilpotence theorem as a key tool

Provides evidence supporting the conjectural framework

Abstract

Motivated by the Bloch-Beilinson conjectures, we formulate a certain covariant weak Lefschetz property for Chow groups. We prove this property in some special cases, using Kimura's nilpotence theorem.