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Local Tate duality : ウィキペディア英語版
Local Tate duality
In Galois cohomology, local Tate duality (or simply local duality) is a duality for Galois modules for the absolute Galois group of a non-archimedean local field. It is named after John Tate who first proved it. It shows that the dual of such a Galois module is the Tate twist of usual linear dual. This new dual is called the (local) Tate dual.
Local duality combined with Tate's local Euler characteristic formula provide a versatile set of tools for computing the Galois cohomology of local fields.
==Statement==
Let ''K'' be a non-archimedean local field, let ''Ks'' denote a separable closure of ''K'', and let ''GK'' = Gal(''Ks''/''K'') be the absolute Galois group of ''K''.

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