English

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.

Keywords

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