Duality theorem for groups of multiplicative type over some function fields

Diego Izquierdo

doi:10.1016/j.crma.2017.01.014

Duality theorem for groups of multiplicative type over some function fields

Titre traduit de la contribution: Dualité pour les groupes de type multiplicatif sur certains corps de fonctions

Diego Izquierdo

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Résumé

Let K be the function field of a smooth projective curve X over a higher-dimensional local field k. 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. In this note, we state and sketch the proof of an arithmetic duality theorem for Tate–Shafarevich groups of groups of multiplicative type over K (and more generally of some two-term complexes of tori over K).

Titre traduit de la contribution	Dualité pour les groupes de type multiplicatif sur certains corps de fonctions
langue originale	Anglais
Pages (de - à)	268-271
Nombre de pages	4
journal	Comptes Rendus Mathematique
Volume	355
Numéro de publication	3
Les DOIs	https://doi.org/10.1016/j.crma.2017.01.014
état	Publié - 1 mars 2017

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10.1016/j.crma.2017.01.014

Contient cette citation

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title = "Duality theorem for groups of multiplicative type over some function fields",

abstract = "Let K be the function field of a smooth projective curve X over a higher-dimensional local field k. 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. In this note, we state and sketch the proof of an arithmetic duality theorem for Tate–Shafarevich groups of groups of multiplicative type over K (and more generally of some two-term complexes of tori over K).",

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AB - Let K be the function field of a smooth projective curve X over a higher-dimensional local field k. 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. In this note, we state and sketch the proof of an arithmetic duality theorem for Tate–Shafarevich groups of groups of multiplicative type over K (and more generally of some two-term complexes of tori over K).

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DO - 10.1016/j.crma.2017.01.014

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Duality theorem for groups of multiplicative type over some function fields

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