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date: 2022-04-08 12:41
modification date: Friday 8th April 2022 12:41:49
title: "tate duality"
aliases: [tate duality]
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# tate duality

In [Galois cohomology](Galois%20cohomology),
$$
H^{r}_\Gal(k; M) \times H^{2-r}_\Gal\left(k; M^{\prime}\right) \rightarrow H^{2}_\Gal\left(k; \GG_{m}\right)=\mathbb{Q} / \mathbb{Z}
$$