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 arbitrary direct sums. In addition, subcategories of A-modules that are closed under taking submodules, extensions, and direct unions are classified via associated prime ideals.
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Krause, H. Thick subcategories of modules over commutative noetherian rings (with an appendix by Srikanth Iyengar). Math. Ann. 340, 733–747 (2008). https://doi.org/10.1007/s00208-007-0166-3
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DOI: https://doi.org/10.1007/s00208-007-0166-3