Thick subcategories

Abstract. We study the thick subcategories of the stable category of finitely generated modules for the principal block of the group algebra of a finite group G over a field of characteristic p. In case G is a p-group we obtain a complete classification of the thick subcategories. The same classification works whenever the nucleus of the cohomology variety is zero. In case the nucleus is nonzero, we describe some examples which lead us to believe that there are always infinitely many thick subcategories concentrated on each nonzero closed homogeneous subvariety of the nucleus. 1. Introduction. A subcategory of a triangulated category is said to be thick, or épaisse, if it is a triangulated subcategory and it is closed under taking direct summands. One product of the deep work of Devinatz, Hop-kins and Smith [8] on stable homotopy theory was a classification of the thick subcategories of the stable homotopy category. This is described i