Complex varieties with infinite Chow groups modulo 2

TL;DR

This paper demonstrates that very general complex abelian 3-folds have infinite Chow groups modulo any prime, providing the first known examples of such varieties with infinite Chow groups modulo 2.

Contribution

It establishes the existence of complex varieties with infinite Chow groups modulo 2, a previously unknown phenomenon in algebraic geometry.

Findings

Chow groups are infinite modulo every prime for very general abelian 3-folds.

First examples of complex varieties with infinite Chow groups modulo 2.

Advances understanding of algebraic cycles in complex geometry.

Abstract

We show that for a very general principally polarized complex abelian 3-fold, the Chow group of algebraic cycles is infinite modulo every prime number. In particular, this gives the first examples of complex varieties with infinite Chow groups modulo 2.