A NOTE ON 1-MOTIVES

Yves André (1)

1 LIFL - Laboratoire d'Informatique Fondamentale de Lille

We prove that for 1-motives defined over an algebraically closed subfield of C, viewed as Nori motives, the motivic Galois group coincides with the Mumford-Tate group. In particular, the Hodge realization of the tannakian category of Nori motives generated by 1-motives is fully faithful. This result extends an earlier result by the author, according to which Hodge cycles on abelian varieties are motivated (a weak form of the Hodge conjecture).

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]; Algèbre commutative [math.AC]

Yves André. A NOTE ON 1-MOTIVES. International Mathematics Research Notices, 2019. ⟨hal-02408019⟩