Torsion 1-cycles and the coniveau spectral sequence

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 ${\HH}$-cohomology the Griffiths group of 1-cycles and the group of torsion cycles algebraically equivalent to zero of arbitrary dimension.

2010 Mathematics Subject Classification: 14C25, 14C15, 14C35

Keywords and Phrases: 1-cycles, Griffiths group, Abel-Jacobi map, coniveau spectral sequence, {\HH}-cohomology, birational invariant

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