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Complexity and varieties for infinitely generated modules, II

Published online by Cambridge University Press:  24 October 2008

D. J. Benson ,
Jon F. Carlson  and
J. Rickard
D. J. Benson
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30602, USA. e-mail address: [email protected]
Jon F. Carlson
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30602, USA. e-mail address: [email protected]
J. Rickard
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW. e-mail address: [email protected]
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Extract

It has now been almost twenty years since Alperin introduced the idea of the complexity of a finitely generated kG-module, when G is a finite group and k is a field of characteristic p > 0. In proving one of the first major results in the area [1], Alperin and Evens demonstrated the connection of the study of complexity for modules to the group cohomology. That connection eventually led to the categorization of modules according to their associated varieties in the maximal ideal spectrum of the cohomology ring H*(G, k). In all of the work that has followed, two principles have proved to be extremely important. The first is that the associated variety of a module is directly related to the structure of the module through the rank variety which is defined by the matrix representation of the module. The second major result is the tensor product theorem which says that the variety associated to a tensor product M ⊗kN is the intersection of the varieties associated to the modules M and N. In this paper we generalize these results to infinitely generated kG-modules.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 4 , November 1996 , pp. 597 - 615
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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