Deligne's duality for de Rham realizations of 1-motives

2005/06/17 by Alessandra Bertapelle, Bertapelle, Alessandra · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.math/0506344

Abstract

We show that the pairing on de Rham realizations of 1-motives in "Theorie di Hodge III", IHES 44, can be defined over any base scheme and we prove that it gives rise to a perfect duality if one is working with a 1-motive and its Cartier dual. Furthermore we study universal extensions of 1-motives and their relation with \natural-extensions.

Cited by

• Canonical extensions of Néron models of Jacobians
• P-adic Period Conjectures for 1-motives: Integration and Linear Relations

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• On the derived category of 1-motives, I
• The generalized Cassels-Tate dual exact sequence for 1-motives
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