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

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 $♮$-extensions.

arXiv comment21 pages. Last section rewritten. New proofs

References in corpus (2)

• Albanese and Picard 1-motives
• Crystalline realizations of 1-motives

Cited by in corpus (1)

• Canonical extensions of Néron models of Jacobians