Finiteness in derived categories of local rings

  • William G. Dwyer

    University of Notre Dame, United States
  • John P. C. Greenlees

    University of Sheffield, United Kingdom
  • Srikanth B. Iyengar

    University of Nebraska-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.

Cite this article

William G. Dwyer, John P. C. Greenlees, Srikanth B. Iyengar, Finiteness in derived categories of local rings. Comment. Math. Helv. 81 (2006), no. 2, pp. 383–432

DOI 10.4171/CMH/56