Carlson's theorem on varieties and transfer (Q1114193)

\textit{J. F. Carlson} [ibid. 44, 99-105 (1987; Zbl 0615.20033)] has proved for finite groups that the variety in spec \(H^{ev}(BG,{\mathbb{F}}_ p)\) defined by the ideal generated by the images of transfers from all subgroups of index divisible by p is the same as the variety defined by the kernel of the restriction to the center of a p-Sylow subgroup. We prove a generalization of this theorem for compact Lie groups. For finite groups the proof specializes to a purely algebraic proof which is a bit shorter and somewhat more direct than Carlson's original proof.