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arxiv: math/0506344 · v3 · submitted 2005-06-17 · 🧮 math.AG

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

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keywords motivesdualityextensionsrealizationsrhambasecartierdefined
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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.

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