Arithmetic Hodge structure and higher Abel-Jacobi maps

Details Arithmetic Hodge structure and higher Abel-Jacobi maps Arithmetic Hodge structure and higher Abel-Jacobi maps

1999-08-05

arxiv.org/abs/math/9908019v1

Mathematics

Algebraic Geometry

Latex2e, 20pages

Scientific paper

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.

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