Skip to Main Content

Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Finite generation of Tate cohomology
HTML articles powered by AMS MathViewer

by Jon F. Carlson, Sunil K. Chebolu and Ján Mináč
Represent. Theory 15 (2011), 244-257
Published electronically: March 14, 2011


Let $G$ be a finite group and let $k$ be a field of characteristic $p$. Given a finitely generated indecomposable nonprojective $kG$-module $M$, we conjecture that if the Tate cohomology $\hat {H}^*(G, M)$ of $G$ with coefficients in $M$ is finitely generated over the Tate cohomology ring $\hat {H}^*(G, k)$, then the support variety $V_G(M)$ of $M$ is equal to the entire maximal ideal spectrum $V_G(k)$. We prove various results which support this conjecture. The converse of this conjecture is established for modules in the connected component of $k$ in the stable Auslander-Reiten quiver for $kG$, but it is shown to be false in general. It is also shown that all finitely generated $kG$-modules over a group $G$ have finitely generated Tate cohomology if and only if $G$ has periodic cohomology.
Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 20C20, 20J06, 55P42
  • Retrieve articles in all journals with MSC (2010): 20C20, 20J06, 55P42
Bibliographic Information
  • Jon F. Carlson
  • Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
  • MR Author ID: 45415
  • Email:
  • Sunil K. Chebolu
  • Affiliation: Department of Mathematics, Illinois State University, Campus box 4520, Normal, Illinois 61790
  • Email:
  • Ján Mináč
  • Affiliation: Department of Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada
  • Email:
  • Received by editor(s): August 17, 2009
  • Received by editor(s) in revised form: March 9, 2010
  • Published electronically: March 14, 2011
  • Additional Notes: The first author is partially supported by a grant from NSF and the third author is supported from NSERC

  • Dedicated: Dedicated to Professor Luchezar Avramov on his sixtieth birthday.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 15 (2011), 244-257
  • MSC (2010): Primary 20C20, 20J06; Secondary 55P42
  • DOI:
  • MathSciNet review: 2781019