Infinite torsion in Griffiths groups

TL;DR

This paper demonstrates the existence of smooth complex projective varieties with infinite 2-torsion in their Griffiths groups, revealing that these torsion subgroups are generally not finitely generated, thus resolving a longstanding problem.

Contribution

It proves the existence of varieties with infinite torsion in Griffiths groups, answering a question posed by Schoen in 1992.

Findings

Existence of varieties with infinite 2-torsion in Griffiths groups

Torsion subgroup of Griffiths groups is not finitely generated in general

Solves a 30-year-old open problem

Abstract

We show that there are smooth complex projective varieties with infinite 2-torsion in their third Griffiths groups. It follows that the torsion subgroup of Griffiths groups is in general not finitely generated, thereby solving a problem of Schoen from 1992.