Carlson's theorem on varieties and transfer
type: Item
instance of: scholarly article
title: Carlson's theorem on varieties and transfer
zbMATH Open document ID: 0663.55007
DOI: 10.1016/0022-4049(89)90026-1
author: Leonard Evens
author: Mark Feshbach
published in: Journal of Pure and Applied Algebra
publication date: 1989-01-01T00:00:00Z
review text: \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.
Mathematics Subject Classification ID: 55R40
Mathematics Subject Classification ID: 57T25
Mathematics Subject Classification ID: 55R12
zbMATH DE Number: 4084565
zbMATH Keywords: cohomology of classifying spaces of compact Lie groups
zbMATH Keywords: variety of prime ideals in the cohomology ring
zbMATH Keywords: ideal generated by the images of transfers from all subgroups of index divisible by p
MaRDI profile type: Publication
full work available at URL: 0022-4049(89)90026-1
OpenAlex ID: W2022666847
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description: scientific article; zbMATH DE number 4084565