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Spaces with Noetherian cohomology

Part of: Homology and cohomology theories Applied homological algebra and category theory Homological algebra Chain conditions, finiteness conditions Fiber spaces and bundles Spectral sequences

Published online by Cambridge University Press:  05 December 2012

Kasper K. S. Andersen ,
Natàlia Castellana ,
Vincent Franjou ,
Alain Jeanneret  and
Jérôme Scherer
Kasper K. S. Andersen
Affiliation:
Centre for Mathematical Sciences, Lunds Tekniska Högskola, Box 118, 22100 Lund, Sweden ([email protected])
Natàlia Castellana
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain ([email protected])
Vincent Franjou
Affiliation:
Laboratoire Jean-Leray, UMR 6629, 2 rue de la Houssinière, BP 92208, 44322 Nantes cedex 3, France ([email protected])
Alain Jeanneret
Affiliation:
Mathematisches Institut, Universität Bern, Sidlerstrasse 5, 3012 Bern, Switzerland ([email protected])
Jérôme Scherer
Affiliation:
École Polytechnique Fédérale de Lausanne, School of Basic Sciences, Mathematics Institute of Geometry and Applications, MA B3 455, Station 8, 1015 Lausanne, Switzerland ([email protected])
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Abstract

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Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? In this paper we provide, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens–Venkov Theorem. We consider the cohomology of a space with coefficients in a module, and we compare Noetherianity over the field with p elements with Noetherianity over the p-adic integers, in the case when the fundamental group is a finite p-group.

Keywords

Noetheriancohomologyuniversal coefficientsclassifying spacep-compact groupsp-local finite groups

MSC classification

Secondary: 55U20: Universal coefficient theorems, Bockstein operator 13E05: Noetherian rings and modules 18G15: Ext and Tor, generalizations, Künneth formula 55N25: Homology with local coefficients, equivariant cohomology 55T10: Serre spectral sequences 55R12: Transfer 55R35: Classifying spaces of groups and $H$-spaces
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 1 , February 2013 , pp. 13 - 25
Copyright
Copyright © Edinburgh Mathematical Society 2012

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