Geodesic
Deligne’s conjecture on 1-motives
Luca Barbieri-Viale1 ; Andreas Rosenschon2 ; Morihiko Saito3
1 Department of Mathematics, University of Rome La Sapienza, Rome, Italy
2 Mathematics Department, University of Buffalo, The State University of New York, Buffalo, NY 14260, United States
3 RIMS Kyoto University<br/>Kyoto 606-8502<br/>Japan
Annals of mathematics, Tome 158 (2003) no. 2, pp. 593-633.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We reformulate a conjecture of Deligne on $1$-motives by using the integral weight filtration of Gillet and Soulé on cohomology, and prove it. This implies the original conjecture up to isogeny. If the degree of cohomology is at most two, we can prove the conjecture for the Hodge realization without isogeny, and even for $1$-motives with torsion.
DOI : 10.4007/annals.2003.158.593

Luca Barbieri-Viale 1 ; Andreas Rosenschon 2 ; Morihiko Saito 3

1 Department of Mathematics, University of Rome La Sapienza, Rome, Italy
2 Mathematics Department, University of Buffalo, The State University of New York, Buffalo, NY 14260, United States
3 RIMS Kyoto University<br/>Kyoto 606-8502<br/>Japan 
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Luca Barbieri-Viale; Andreas Rosenschon; Morihiko Saito. Deligne’s conjecture on 1-motives. Annals of mathematics, Tome 158 (2003) no. 2, pp. 593-633. doi : 10.4007/annals.2003.158.593. http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.158.593/

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