# Deligne’s conjecture on 1-motives

### Abstract

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.

## Authors

Luca Barbieri-Viale

Department of Mathematics, University of Rome La Sapienza, Rome, Italy

Andreas Rosenschon

Mathematics Department, University of Buffalo, The State University of New York, Buffalo, NY 14260, United States

Morihiko Saito

RIMS Kyoto University
Kyoto 606-8502
Japan