Algebraic invariants for finite group actions. I: Varieties
type: Item
instance of: scholarly article
title: Algebraic invariants for finite group actions. I: Varieties
zbMATH Open document ID: 0809.57022
author: Amir H. Assadi
published in: Advances in Mathematics
publication date: 1995-04-03T00:00:00Z
review text: The paper concerns applications of shifted subgroups, cohomological support varieties, rank varieties and complexity to finite transformation groups. The author studies the cohomology of a finite group with coefficients in a cochain complex (see, e.g., \textit{K. S. Brown}, Cohomology of groups (1982; Zbl 0584.20036), Ch. VII, Sec. 5) with emphasis on elementary abelian \(p\)-groups and cochain complexes with finitely generated cohomology. He proves an algebraic version of the Localization Theorem of Borel, Hsiang, Quillen, which can be applied topologically to elementary abelian \(p\)-group actions on spaces with finite dimensional mod. \(p\) cohomology. Among the various applications there are (1) a Rim-Chouinard-Dade type projectivity criterion for a \(G\)- module arising as the reduced homology of a \(G\)-space; (2) necessary and sufficient conditions for certain CW-complexes to be finitely dominated; and (3) some Borsuk-Ulam type theorems.
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 55P91
Mathematics Subject Classification ID: 55P60
Mathematics Subject Classification ID: 20J06
zbMATH DE Number: 490808
zbMATH Keywords: elementary abelian \(p\)-groups
zbMATH Keywords: localization
zbMATH Keywords: elementary abelian \(p\)-group actions on spaces with finite dimensional mod. \(p\) cohomology
zbMATH Keywords: shifted subgroups
zbMATH Keywords: cohomological support varieties
zbMATH Keywords: rank varieties
zbMATH Keywords: complexity
zbMATH Keywords: finite transformation groups
zbMATH Keywords: cohomology of a finite group with coefficients in a cochain complex
zbMATH Keywords: projectivity criterion
zbMATH Keywords: finitely dominated
zbMATH Keywords: Borsuk-Ulam
MaRDI profile type: Publication
full work available at URL: aima.1993.1034
OpenAlex ID: W2048494475
DOI: 10.1006/AIMA.1993.1034
description: scientific article; zbMATH DE number 490808