Thick subcategories of modules over commutative rings (with an appendix by Srikanth Iyengar) Henning Krause 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.