= Witt residue sequence
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{title2=$\partial_K:\operatorname{Br}(K)\to H^1(k,\mathbb Q/\mathbb Z)$}
= Witt theorem for the Brauer group
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{synonym}
For a complete discretely valued field $K$ with perfect <residue field> $k$, there is a split exact sequence $0\to\operatorname{Br}(k)\to\operatorname{Br}(K)\xrightarrow{\partial_K}H^1(k,\mathbb Q/\mathbb Z)\to0$. The residue is canonical. A <uniformizer> chooses a splitting $\chi\mapsto(\chi,\pi)$; this choice does not make the residue itself noncanonical.
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