Deligne's conjecture on extensions of 1-motives

2009/06/11 by Cristiana Bertolin, Bertolin, Cristiana
Mathematics · #Algebraic Geometry and Number Theory #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0906.2179

Abstract

We introduce the notion of extension of 1-motives. Using the dictionary between strictly commutative Picard stacks and complexes of abelian sheaves concentrated in degrees -1 and 0, we check that an extension of 1-motives induces an extension of the corresponding strictly commutative Picard stacks. We compute the Hodge, the de Rham and the l-adic realizations of an extention of 1-motives. Using these results we can prove Deligne's conjecture on extensions of 1-motives.

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• On the derived category of 1-motives, I
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• From Jacobians to one-motives: exposition of a conjecture of Deligne