Corestriction map in group cohomology
= Corestriction map in group cohomology
{title2=$\operatorname{Cor}_U^G:H^q(U,M)\to H^q(G,M)$}
For an open finite-index subgroup $U$ of a <profinite group> $G$ and a discrete $G$-module $M$, cohomological transfer gives $\operatorname{Cor}_U^G:H^q(U,M)\to H^q(G,M)$. In degree zero it is the sum over cosets, or the norm for multiplicative coefficients. It is transitive and satisfies $\operatorname{Cor}\operatorname{Res}=[G:U]$ and the cup-product projection formula.