Remarks on hard Lefschetz conjectures on Chow groups

TL;DR

This paper introduces two new Hard Lefschetz type conjectures on Chow groups, proves them in specific cases, and relates them to existing conjectures for abelian varieties, advancing understanding in algebraic geometry.

Contribution

It formulates new conjectures on Chow groups, proves them in special cases, and links them to established conjectures for abelian varieties, providing new insights.

Findings

Conjectures hold for certain cases of Chow groups.

Equivalence established between new conjectures and Beauville-Murre conjectures for abelian varieties.

Progress in understanding the structure of Chow groups in algebraic geometry.

Abstract

We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we shall show they are equivalent to well-known conjectures of Beauville and Murre.