Thick subcategories of modules over commutative rings

TL;DR

This paper classifies all thick subcategories of modules over a commutative noetherian ring, linking support of complexes to their cohomology, and provides a comprehensive structural understanding of these subcategories.

Contribution

It offers a complete classification of thick subcategories of modules over commutative noetherian rings based on support properties, connecting complex support with cohomology support.

Findings

Classification of all thick subcategories of A-modules

Support of a complex determines support of its cohomology

Thick subcategories are characterized by support conditions

Abstract

For a commutative noetherian ring A, we compare the support of a complex of A-modules with the support of its cohomology. This leads to a classification of all full subcategories of A-modules which are thick (that is, closed under taking kernels, cokernels, and extensions) and closed under taking direct sums.