Restriction and corestriction of local Brauer invariants (${\mathrm{inv}}_L\mathrm{Res}=[L:K]{\mathrm{inv}}_K,{\mathrm{inv}}_K\mathrm{Cor}={\mathrm{inv}}_L$)

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.