The thick subcategory generated by the trivial module


Jon F. Carlson

(University of Georgia)


Northeastern University

450 Dodge Hall

4:30 p.m., Thursday, April 16, 1998

Abstract: We consider the stable category of kG-modules modulo projectives, where G is a finite group and k is a field of characteristic p> 0. The thick subcategory K generated by the trivial module k consists of all modules that can be pieced together by extension from k and from On(k) where On(k) is the kernel of the nth boundary map in a complete resolution of k. There is a sense in which all cohomology takes place in K, and in the subcategory K the module theory is reasonably well behaved. The varieties defined by ordinary cohomology measure the homological invariants of modules. A classification of the thick subcategories of K can be reasonably given. Even the self-equivalences of K can be characterized in a nice way. In this lecture I will try to survey some of the recent results in the area and present some examples to illustrate the points.

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