= Local fundamental class
{title2=$u_{L/K}\in H^2(\operatorname{Gal}(L/K),L^\times),\quad\operatorname{inv}_K(u_{L/K})=1/[L:K]$}
For a finite <Galois extension> $L/K$ of non-Archimedean <local fields>, its relative <Brauer group> is the kernel of restriction $\operatorname{Br}(K)\to\operatorname{Br}(L)$ and identifies with $H^2(\operatorname{Gal}(L/K),L^\times)$. Restriction multiplies the <local Brauer invariant> by $[L:K]$. This kernel is therefore cyclic of order $[L:K]$, and the indicated class is its distinguished generator. In an <unramified extension> with <arithmetic Frobenius> generator it is represented by the <cyclic algebra> with parameter a <uniformizer>.
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