= Norm projection formula for cyclic Brauer pairings
{title2=$\operatorname{Cor}(\operatorname{Res}\chi,a)=(\chi,N_{L/K}a)$}
For a finite extension $L/K$, an unramified or general cyclic character $\chi$ over $K$, and $a\in L^{\times}$, transfer satisfies $\operatorname{Cor}_{L/K}(\operatorname{Res}\chi,a)=(\chi,N_{L/K}a)$. It is the cup-product projection formula combined with the <field norm> on multiplicative degree-zero coefficients. With the norm definition of Brauer transfer it also covers purely inseparable steps.
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