Deligne's Conjecture on 1-Motives
Luca Barbieri-Viale, Andreas Rosenschon, Morihiko Saito
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.
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