From Jacobians to one-motives: exposition of a conjecture of Deligne

Details From Jacobians to one-motives: exposition of a conjecture of Deligne From Jacobians to one-motives: exposition of a conjecture of Deligne

2001-02-05

arxiv.org/abs/math/0102033v1

The arithmetic and geometry of algebraic cycles. (Banff, 1998) CRM Proceedings & Lecture Notes, 24., AMS

Mathematics

Algebraic Geometry

19 pages, no figures

Scientific paper

Deligne has conjectured that certain mixed Hodge theoretic invariants of complex algebraic invariants are motivic. This conjecture specializes to an algebraic construction of the Jacobian for smooth projective curves, which was done by A. Weil. The conjecture (and one-motives) are motivated by means of Jacobians, generalized Jacobians of Rosenlicht, and Serre's generalized Albanese varieties. We discuss the connections with the Hodge and the generalized Hodge conjecture. We end with some applications to number theory by providing partial answers to questions of Serre, Katz and Jannsen.

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