= Local Brauer invariant
{title2=$\operatorname{inv}_K:\operatorname{Br}(K)\xrightarrow{\sim}\mathbb Q/\mathbb Z$}
= Brauer invariant of a local field
{c}
{synonym}
For a <local field> with finite <residue field>, evaluate the Witt residue character on arithmetic Frobenius. This gives $\operatorname{inv}_K:\operatorname{Br}(K)\cong\mathbb Q/\mathbb Z$. For the unramified degree-$m$ <cyclic algebra> with arithmetic Frobenius generator and parameter $a$, the invariant is $v_K(a)/m$. Its reduced denominator is the index of the division representative.
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