English

Deligne's Conjecture on 1-Motives

Algebraic Geometry 2009-09-25 v4

Abstract

We reformulate a conjecture of Deligne on 1-motives by using the integral weight filtration of Gillet and Soul\'e 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.

Keywords

Cite

@article{arxiv.math/0102150,
  title  = {Deligne's Conjecture on 1-Motives},
  author = {Luca Barbieri-Viale and Andreas Rosenschon and Morihiko Saito},
  journal= {arXiv preprint arXiv:math/0102150},
  year   = {2009}
}

Comments

41 pages published version

R2 v1 2026-07-22T16:37:23.872Z