# 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