Galois theory of thick subcategories in modular representation theory

D. J. Benson, J. F. Carlson, and J. Rickard [1997, Fund. Math. 153, 59-80] classified the tenser-closed thick subcategories of finite-dimensional representations of finite groups over algebraically closed fields. In this paper, we remove the algebraically closed hypothesis by applying some Galois theory. Our methods apply more generally to finite-dimensional cocommutative Hopf algebras over a field. Thus they allow us to drop the algebraically closed hypothesis in the classification of thick subcategories of modules over finite-dimensional sub-Hopf algebras of the Steenrod algebra as well, (C) 2000 Academic Press.