= Restriction and corestriction of local Brauer invariants
{title2=$\operatorname{inv}_L\operatorname{Res}=[L:K]\operatorname{inv}_K,\quad\operatorname{inv}_K\operatorname{Cor}=\operatorname{inv}_L$}
For a finite extension of <local fields> $L/K$, restriction multiplies the <local Brauer invariant> by $[L:K]$ and corestriction preserves it. For restriction, the residue-character value multiplies by the <residue degree> and the parameter valuation by the <ramification index>. For corestriction, lift the residue character using divisibility of $\mathbb Q/\mathbb Z$ and use the <norm projection formula for cyclic Brauer pairings>.
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