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Module categories for group algebras over commutative rings

Published online by Cambridge University Press:  06 March 2013

Dave Benson ,
Srikanth B. Iyengar  and
Henning Krause
Dave Benson
Affiliation:
Institute of Mathematics, University of Aberdeen, King's College, Aberdeen AB24 3UE, ScotlandU.K.d.j.benson@abdn.ac.uk
Srikanth B. Iyengar
Affiliation:
Department of Mathematics, University of Nebraska, Lincoln, NE 68588, U.S.A.s.b.iyengar@unl.edu
Henning Krause
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany. hkrause@math.uni-bielefeld.de
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Abstract

We develop a suitable version of the stable module category of a finite group G over an arbitrary commutative ring k. The purpose of the construction is to produce a compactly generated triangulated category whose compact objects are the finitely presented kG-modules. The main idea is to form a localisation of the usual version of the stable module category with respect to the filtered colimits of weakly injective modules. There is also an analogous version of the homotopy category of weakly injective kG-modules and a recollement relating the stable category, the homotopy category, and the derived category of kG-modules.

Keywords

Group algebraweakly projective moduleweakly injective modulestable categoryhomotopy categoryderived category20C2018E3020C0520J06
Type
Research Article
Information
Journal of K-Theory , Volume 11 , Issue 2 , April 2013 , pp. 297 - 329
Copyright
Copyright © ISOPP 2013 

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Footnotes

with an appendix by Greg Stevenson

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