Theodosis Alexandrou (Universität Hannover)

The Griffiths group $Griff^{i}(X)$ of a smooth complex projective variety $X$ is the group of nullhomologous codimension$-i$ cycles on $X$ modulo algebraic equivalence. Recently Schreieder gave the first examples of smooth complex projective varieties $X$ for which the Griffiths group has infinite torsion. In his examples the infinitely many torsion classes are of order 2. In this talk we show that for any integer $n\geq 2$, there is a smooth complex projective $5-$fold $X$ whose third Griffiths group contains infinitely many torsion elements of order $n$.