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arXiv:math/9908019 [math.AG]AbstractReferencesReviewsResources

Arithmetic Hodge structure and higher Abel-Jacobi maps

Masanori Asakura

Published 1999-08-05Version 1

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.

Comments: Latex2e, 20pages
Categories: math.AG
Subjects: 14C30, 32S35
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