One-motives were introduced by Deligne in 1974 , as a generalization of the theory of semiabelian varieties. Viewed today, after Voevodsky’s theory of mixed motives , 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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Luca Barbieri-Viale, Hélène Esnault, David Harari, Mini-Workshop: 1-Motives. Oberwolfach Rep. 7 (2010), no. 4, pp. 3237–3267DOI 10.4171/OWR/2010/55