Geodesic
Abelian varieties for function fields of curves over local fields
Documenta mathematica, Tome 22 (2017), pp. 297-361
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Let K be the function field of a smooth projective curve X over a p-adic field or over C((t)). We define Tate-Shafarevich groups of a commutative group scheme via cohomology classes locally trivial at each completion of K coming from a closed point of X. We prove arithmetic duality theorems for Tate-Shafarevich groups of abelian varieties over K.
DOI : 10.4171/dm/567
Classification : 11G45, 11S25, 14F20, 14G05, 14G20, 14H05, 14K15
Mots-clés : abelian varieties, function fields, arithmetic duality, Galois cohomology 
@article{10_4171_dm_567,
     author = {Diego Izquierdo},
     title = {Abelian varieties for function fields of curves over local fields},
     journal = {Documenta mathematica},
     pages = {297--361},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/567},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/567/}
}
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%J Documenta mathematica
%D 2017
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Diego Izquierdo. Abelian varieties for function fields of curves over local fields. Documenta mathematica, Tome 22 (2017), pp. 297-361. doi: 10.4171/dm/567

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