Finiteness in derived categories of local rings

Details Finiteness in derived categories of local rings Finiteness in derived categories of local rings

2004-04-02

arxiv.org/abs/math/0404034v2

Mathematics

Commutative Algebra

40 pages. Minor revisions. To appear in Commentarii Math. Helvetici

Scientific paper

New homotopy invariant finiteness conditions on modules over commutative rings are introduced, and their properties are studied systematically. A number of finiteness results for classical homological invariants like flat dimension, injective dimension, and Gorenstein dimension, are established. It is proved that these specialize to give results concerning modules over complete intersection local rings. A noteworthy feature is the use of techniques based on thick subcategories of derived categories.

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