Classifying thick subcategories over a Koszul complex via the curved BGG correspondence

Abstract

In this work we classify the thick subcategories of the bounded derived category of dg modules over a Koszul complex on any list of elements in a regular ring. This simultaneously recovers a theorem of Stevenson when the list of elements is a regular sequence and the classification of thick subcategories for an exterior algebra over a field (via the BGG correspondence). One of the major ingredients is a classification of thick tensor submodules of perfect curved dg modules over a commutative noetherian graded ring concentrated in even degrees, recovering a theorem of Hopkins and Neeman. We give several consequences of the classification result over a Koszul complex, one being that the lattice of thick subcategories of the bounded derived category is fixed by Grothendieck duality.