Arithmetic Hodge structure and higher Abel-Jacobi maps
Algebraic Geometry
2007-05-23 v1
Abstract
In this paper, we show some applications to algebraic cycles by using higher Abel-Jacobi maps which were defined in [the author: Motives and algebraic de Rham cohomology]. In particular, we prove that the Beilinson conjecture on algebraic cycles over number fields implies the Bloch conjecture on zero-cycles on surfaces. Moreover, we construct a zero-cycle on a product of curves whose Mumford invariant vanishes, but not higher Abel-Jacobi invariant.
Cite
@article{arxiv.math/9908019,
title = {Arithmetic Hodge structure and higher Abel-Jacobi maps},
author = {Masanori Asakura},
journal= {arXiv preprint arXiv:math/9908019},
year = {2007}
}
Comments
Latex2e, 20pages