Commentarii Mathematici Helvetici


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Volume 81, Issue 2, 2006, pp. 383–432
DOI: 10.4171/CMH/56

Finiteness in derived categories of local rings

William G. Dwyer (1), John P. C. Greenlees (2) and Srikanth B. Iyengar (3)

(1) Department of Mathematics, University of Notre Dame, IN 46556-4618, NOTRE DAME, UNITED STATES
(2) Pure Mathematics Department, University of Sheffield, Hicks Building, Hounsfield Road, S3 7RH, SHEFFIELD, UNITED KINGDOM
(3) Department of Mathematics, University of Nebraska-Lincoln, NE 68588-0130, LINCOLN, UNITED STATES

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.

Keywords: Complete intersections, Gorenstein rings, homological dimensions, perfect complexes, thick subcategories