JournalsowrVol. 7 / No. 4DOI 10.4171/owr/2010/55

Mini-Workshop: 1-Motives

  • Luca Barbieri-Viale

    Università di Milano, Italy
  • Hélène Esnault

    FU Berlin, Germany
  • David Harari

    Université Paris-Sud, Orsay, France
Mini-Workshop: 1-Motives cover

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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.