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Toshiro Hiranouchi
Class field theory for open curves over local fields
Journal de théorie des nombres de Bordeaux, 30 no. 2 (2018), p. 501-524, doi: 10.5802/jtnb.1036
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Class. Math.: 11R37, 11R58
Mots clés: Class field theory, local fields

Résumé - Abstract

Nous étudions la théorie des corps de classes des courbes ouvertes sur un corps local. Après avoir introduit l’application de réciprocité nous déterminons son noyau et son conoyau. La duale de Pontrjagin de l’application de réciprocitIé est également étudiée. Cela nous donne, sous certaines hypothèses, une correspondance bijective entre l’ensemble des revêtements étales abéliens et l’ensemble des sous-groupes ouverts d’indice fini du groupe des classes d’idèles.

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