TY - JOUR
T1 - On Gorenstein projective, injective and flat dimensions-A functorial description with applications
AU - Christensen, Lars Winther
AU - Frankild, Anders
AU - Holm, Henrik
N1 - Funding Information:
✩ Part of this work was done at MSRI during the spring semester of 2003, when the authors participated in the Program in Commutative Algebra. We thank the institution and program organizers for a very stimulating research environment. * Corresponding author. Current address: Department of Mathematics, University of Nebraska, Lincoln, NE 68588, USA. E-mail addresses: winther@math.unl.edu (L.W. Christensen), frankild@math.ku.dk (A. Frankild), holm@imf.au.dk (H. Holm). 1 The author was partly supported by a grant from the Danish Natural Science Research Council. 2 The author was supported by Lundbeck Fonden, the Danish Natural Science Research Council, and Mathematical Sciences Research Institute (MSRI). 3 Current address: Department of Mathematical Sciences, University of Aarhus, Ny Munkegade Bldg. 530, DK-8000 Aarhus C, Denmark.
PY - 2006/8/1
Y1 - 2006/8/1
N2 - Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings. As opposed to their classical counterparts, these dimensions do not immediately come with practical and robust criteria for finiteness, not even over commutative noetherian local rings. In this paper we enlarge the class of rings known to admit good criteria for finiteness of Gorenstein dimensions: It now includes, for instance, the rings encountered in commutative algebraic geometry and, in the noncommutative realm, k-algebras with a dualizing complex.
AB - Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings. As opposed to their classical counterparts, these dimensions do not immediately come with practical and robust criteria for finiteness, not even over commutative noetherian local rings. In this paper we enlarge the class of rings known to admit good criteria for finiteness of Gorenstein dimensions: It now includes, for instance, the rings encountered in commutative algebraic geometry and, in the noncommutative realm, k-algebras with a dualizing complex.
KW - Auslander categories
KW - Bass formula
KW - Chouinard formula
KW - Dualizing complex
KW - Foxby equivalence
KW - Gorenstein flat dimension
KW - Gorenstein injective dimension
KW - Gorenstein projective dimension
UR - http://www.scopus.com/inward/record.url?scp=33646789161&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2005.12.007
DO - 10.1016/j.jalgebra.2005.12.007
M3 - Article
AN - SCOPUS:33646789161
SN - 0021-8693
VL - 302
SP - 231
EP - 279
JO - Journal of Algebra
JF - Journal of Algebra
IS - 1
ER -