Deligne's Conjecture on 1-Motives

Details Deligne's Conjecture on 1-Motives Deligne's Conjecture on 1-Motives

2001-02-19

arxiv.org/abs/math/0102150v4

Ann. of Math. (2), Vol. 158 (2003), no. 2, 593--633

Mathematics

Algebraic Geometry

41 pages published version

Scientific paper

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.

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