Duality for cohomology of curves with coefficients in abelian varieties

Abstract

In this paper, we formulate and prove a duality for cohomology of curves over perfect fields of positive characteristic with coefficients in Neron 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 non-degeneracy of the height pairing and finiteness of crystalline cohomology. All these ingredients are organized under the formalism of the rational etale site developed earlier.

79 pages. Accepted for publication in Nagoya Mathematical Journal

References in corpus (2)

• Artin-Mazur-Milne duality for fppf cohomology
• Neron models of 1-motives and duality

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• Arithmetic duality for two-dimensional local rings with perfect residue field
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• Class field theory, Hasse principles and Picard-Brauer duality for two-dimensional local rings
• An improvement of the duality formalism of the rational etale site
• On $\mu$-invariants and isogenies for abelian varieties over function fields
• Finiteness and cofiniteness of fine Selmer groups over function fields