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tate duality
In Galois cohomology, \begin{align*} H^{r}_{ \mathsf{Gal}} (k; M) \times H^{2-r}_{ \mathsf{Gal}} \left(k; M^{\prime}\right) \rightarrow H^{2}_{ \mathsf{Gal}} \left(k; {\mathbf{G}}_{m}\right)=\mathbb{Q} / \mathbb{Z} \end{align*}