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arXiv · 0906.2179

Deligne's conjecture on extensions of 1-motives

Cristiana Bertolin
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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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Cristiana Bertolin. 2010-04-12. Deligne's conjecture on extensions of 1-motives. https://arxiv.org/abs/0906.2179

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