Pages 593-633 from Volume 158 (2003), Issue 2 by 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.
Received: 22 May 2001
Accepted: 20 May 2002
Published online: September 2003
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