Smash-nilpotent cycles on abelian 3-folds

TL;DR

This paper proves that all homologically trivial algebraic cycles on 3-dimensional abelian varieties become nilpotent when repeatedly intersected, advancing understanding of algebraic cycles in complex geometry.

Contribution

It establishes that homologically trivial cycles on abelian 3-folds are smash-nilpotent, a significant step in the study of algebraic cycles and their equivalence relations.

Findings

Homologically trivial cycles are smash-nilpotent on abelian 3-folds.

Supports conjectures relating to algebraic cycles and their nilpotency.

Enhances understanding of the structure of algebraic cycles in complex algebraic geometry.

Abstract

We show that homologically trivial algebraic cycles on a 3-dimensional abelian variety are smash-nilpotent.