2001/02/05 by Niranjan Ramachandran
Mathematics · #math.AG #math.KT #msc:11Gxx #msc:14C25 #msc:14C30 #msc:14F99
published as The arithmetic and geometry of algebraic cycles. (Banff, 1998) CRM Proceedings & Lecture Notes, 24., AMS · 19 pages, no figures
arxiv created 2001/02/05 · arxiv updated 2009/11/30
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.