Abelian varieties for function fields of curves over local fields

  • Diego Izquierdo

    École Normale Supérieure 45 Rue d'Ulm 75005 Paris, France
Abelian varieties for function fields of curves over local fields cover
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Abstract

Let be the function field of a smooth projective curve over a -adic field or over . We define Tate-Shafarevich groups of a commutative group scheme via cohomology classes locally trivial at each completion of coming from a closed point of . We prove arithmetic duality theorems for Tate-Shafarevich groups of abelian varieties over .

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Diego Izquierdo, Abelian varieties for function fields of curves over local fields. Doc. Math. 22 (2017), pp. 297–361

DOI 10.4171/DM/567