Classifying Serre subcategories of finitely presented modules

Abstract

Given a commutative coherent ring R R , a bijective correspondence between the thick subcategories of perfect complexes D per ( R ) \mathcal D_{\operatorname {per}}(R) and the Serre subcategories of finitely presented modules is established. To construct this correspondence, properties of the Ziegler and Zariski topologies on the set of isomorphism classes of indecomposable injective modules are used in an essential way.