One-motives were introduced by Deligne in 1974 [10], as a generalization of the theory of semiabelian varieties. Viewed today, after Voevodsky’s theory of mixed motives [31], it can be understood as motives of level ≤1. While Voevosdky’s more general theory of mixed motives contains deep conjectures which at present seem to be out of reach, one-motives are much more accessible. In this mini-workshop, recent progresses were discussed: various aspects of one-motives and their realizations were explained, some applications in arithmetic algebraic geometry were given.
Motives / L. Barbieri Viale, H. Esnault, D. Harari. - In: OBERWOLFACH REPORTS. - ISSN 1660-8933. - 7:4(2010), pp. 3237-3267. (Intervento presentato al convegno Mini-Workshop: Motives tenutosi a Oberwolfach nel 2010) [10.4171/OWR/2010/55].
Motives
L. Barbieri VialePrimo
;
2010
Abstract
One-motives were introduced by Deligne in 1974 [10], as a generalization of the theory of semiabelian varieties. Viewed today, after Voevodsky’s theory of mixed motives [31], it can be understood as motives of level ≤1. While Voevosdky’s more general theory of mixed motives contains deep conjectures which at present seem to be out of reach, one-motives are much more accessible. In this mini-workshop, recent progresses were discussed: various aspects of one-motives and their realizations were explained, some applications in arithmetic algebraic geometry were given.
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