Some nilpotence theorems for algebraic cycles

TL;DR

This paper proves a nilpotence theorem for algebraic cycles using Deligne's results and applies it to establish torsion nilpotence for correspondences on surfaces, advancing understanding of algebraic cycle behavior.

Contribution

It introduces a nilpotence theorem for algebraic cycles based on Deligne's fundamental results and extends it to torsion nilpotence for surface correspondences.

Findings

Established a nilpotence theorem for algebraic cycles.

Proved torsion nilpotence for correspondences on surfaces.

Enhanced understanding of algebraic cycle nilpotence properties.

Abstract

Using fundamental results of Deligne, we prove a nilpotence theorem for algebraic cycles and use this to prove a torsion nilpotence result for correspondences on surfaces.