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DUALITY FOR COHOMOLOGY OF CURVES WITH COEFFICIENTS IN ABELIAN VARIETIES

Part of: Algebraic number theory: global fields (Co)homology theory Arithmetic algebraic geometry

Published online by Cambridge University Press:  19 December 2018

TAKASHI SUZUKI
TAKASHI SUZUKI*
Affiliation:
Department of Mathematics, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan email tsuzuki@gug.math.chuo-u.ac.jp
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Abstract

In this paper, we formulate and prove a duality for cohomology of curves over perfect fields of positive characteristic with coefficients in Néron models of abelian varieties. This is a global function field version of the author’s previous work on local duality and Grothendieck’s duality conjecture. It generalizes the perfectness of the Cassels–Tate pairing in the finite base field case. The proof uses the local duality mentioned above, Artin–Milne’s global finite flat duality, the nondegeneracy of the height pairing and finiteness of crystalline cohomology. All these ingredients are organized under the formalism of the rational étale site developed earlier.

MSC classification

Primary: 11G10: Abelian varieties of dimension $> 1$
Secondary: 11R58: Arithmetic theory of algebraic function fields 14F20: Étale and other Grothendieck topologies and (co)homologies
Type
Article
Information
Nagoya Mathematical Journal , Volume 240 , December 2020 , pp. 42 - 149
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Copyright
© 2018 Foundation Nagoya Mathematical Journal

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Footnotes

The author is a Research Fellow of Japan Society for the Promotion of Science.

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