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Deligne's duality for de Rham realizations of 1‐motives
Author(s) -
Bertapelle Alessandra
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610816
Subject(s) - mathematics , duality (order theory) , dual (grammatical number) , pure mathematics , relation (database) , base (topology) , scheme (mathematics) , mathematical analysis , linguistics , philosophy , computer science , database
Let M be a 1‐motive over a base scheme S and M ′ its Cartier dual. We show the existence of a canonical duality between the de Rham realizations of M and M ′; this generalizes a result in [5]. Furthermore, we study universal extensions of 1‐motives and their relation with ♮‐extensions (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)