Stably thick subcategories of modules over Hopf algebras

by Mark Hovey and John Palmieri


AMS Classification: 20C05, 20J05,18E30,18G35, 55P42

We discuss a general method for classifying certain subcategories of the
category of finite-dimensional modules over a finite-dimensional
cocommutative Hopf algebra B.  Our method is based on that of
Benson-Carlson-Rickard, who classify such
subcategories when B=kG, the group ring of a finite group G over
an algebraically closed field k.  We get a similar classification when
B is a finite sub-Hopf algebra of the mod 2 Steenrod algebra, with
scalars extended to the algebraic closure of Z/2.  Along the way,
we prove a Quillen stratification theorem for cohomological varieties of
modules over any B, in terms of quasi-elementary sub-Hopf algebras of
B.