Torsion 1-cycles and the coniveau spectral sequence

Abstract

We relate the torsion part of the Abel-Jacobi kernel in the Griffiths group of 1-cycles to a birational invariant analogous to the degree 4 unramified cohomology and an invariant associated to the generalized Hodge conjecture in degree $2\dim (X)-3$. We also describe in terms of $\mathcal{H}$-cohomology the Griffiths group of 1-cycles and the group of torsion cycles algebraically equivalent to zero of arbitrary dimension.