2004/04/02 by W. Dwyer, Dwyer, W., J. P. C. Greenlees +3 · 1 citation
Mathematics · #13D05 #13D99 (primary). 18E30 #18G99 (secondary) #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.CT #msc:13D05 #msc:13D99 #msc:18E30 #msc:18G99
paper · pdf · doi:10.48550/arxiv.math/0404034
40 pages. Minor revisions. To appear in Commentarii Math. Helvetici
arxiv created 2005/07/09 · arxiv updated 2009/12/01
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.