Carlson's theorem on varieties and transfer
\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.
cohomology of classifying spaces of compact Lie groups
variety of prime ideals in the cohomology ring
ideal generated by the images of transfers from all subgroups of index divisible by p
scientific article; zbMATH DE number 4084565
scientific article