Torsion 1-cycles and the coniveau spectral sequence (Q683767)

Summary: 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.