Varieties and transfers (Q1820871)

Let k be a field of characteristic \(p\neq 0\) and let G be a finite group. Let \(V_ G(k)\) be the set of all maximal ideals of the cohomology algebra \(H^*(G,k)\). Let Z denote the center of a p-Sylow subgroup P of G and let \(J=J(k)\) denote the sum of the images of \(H^*(H,k)\) under the transfer (or corestriction) maps from H to k as H ranges over all subgroups with index divisible by p. J is then an ideal of \(H^*(G,k)\) (the transfer map is not a ring homomorphism). If \(V_ G(J)\subseteq V_ G(k)\) denotes the support of \(H^*(G,k)/J\), then the author proves: Theorem. \(V_ G(J)=res^*_{G,Z}(V_ Z(k))\).