Finite generation of Tate cohomology
Authors:
Jon F. Carlson, Sunil K. Chebolu and Ján Mináč
Journal:
Represent. Theory 15 (2011), 244257
MSC (2010):
Primary 20C20, 20J06; Secondary 55P42
Published electronically:
March 14, 2011
MathSciNet review:
2781019
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: Let be a finite group and let be a field of characteristic . Given a finitely generated indecomposable nonprojective module , we conjecture that if the Tate cohomology of with coefficients in is finitely generated over the Tate cohomology ring , then the support variety of is equal to the entire maximal ideal spectrum . We prove various results which support this conjecture. The converse of this conjecture is established for modules in the connected component of in the stable AuslanderReiten quiver for , but it is shown to be false in general. It is also shown that all finitely generated modules over a group have finitely generated Tate cohomology if and only if has periodic cohomology.
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Additional Information
Jon F. Carlson
Affiliation:
Department of Mathematics, University of Georgia, Athens, Georgia 30602
Email:
jfc@math.uga.edu
Sunil K. Chebolu
Affiliation:
Department of Mathematics, Illinois State University, Campus box 4520, Normal, Illinois 61790
Email:
schebol@ilstu.edu
Ján Mináč
Affiliation:
Department of Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada
Email:
minac@uwo.ca
DOI:
http://dx.doi.org/10.1090/S10884165201100385X
PII:
S 10884165(2011)00385X
Keywords:
Tate cohomology,
finite generation,
periodic modules,
support varieties,
stable module category,
almost split sequence
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.
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
