Torsion 1-cycles and the coniveau spectral sequence

TL;DR

This paper explores the relationship between torsion 1-cycles, the Abel-Jacobi kernel, and spectral sequences, providing new insights into algebraic and Hodge-theoretic invariants of algebraic varieties.

Contribution

It establishes connections between torsion 1-cycles, unramified cohomology, and the generalized Hodge conjecture, advancing understanding of the Griffiths group and related invariants.

Findings

Relates torsion Abel-Jacobi kernel to birational invariants.

Describes Griffiths group and torsion cycles via H-cohomology.

Links algebraic cycles to Hodge-theoretic invariants.

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 2dim(X)-3. We also describe in terms of H-cohomology the Griffiths group of 1-cycles and the group of torsion cycles algebraically equivalent to zero of arbitrary dimension.