Algebraic Cycles and Mumford-Griffiths Invariants

Abstract

Let $X$ be a projective algebraic manifold and let $C{H}^r(X)$ be the Chow group of algebraic cycles of codimension $r$ on $X$, modulo rational equivalence. Working with a candidate Bloch-Beilinson filtration $\{F^{\nu }{\}}_{\nu \ge 0}$ on $C{H}^r(X)\otimes \mathbb{Q}$ due to the second author, we construct a space of arithmetic Hodge theoretic invariants $\nabla J^{r,\nu }(X)$ and corresponding map ${\varphi }_X^{r,\nu }:G{r}_F^{\nu }C{H}^r(X)\otimes \mathbb{Q}\to \nabla J^{r,\nu }(X)$, and determine conditions on $X$ for which the kernel and image of ${\varphi }_X^{r,\nu }$ are ``uncountably large''.

39 pages, To appear in the American Journal of Mathematics

References in corpus (1)

• Higher Abel-Jacobi maps for 0-cycles