TY - JOUR
T1 - Vanishing of cohomology over Cohen-Macaulay rings
AU - Christensen, Lars Winther
AU - Holm, Henrik
PY - 2012/11
Y1 - 2012/11
N2 - A 2003 counterexample to a conjecture of Auslander brought attention to a family of rings-colloquially called AC rings-that satisfy a natural condition on vanishing of cohomology. Several results attest to the remarkable homological properties of AC rings, but their definition is barely operational, and it remains unknown if they form a class that is closed under typical constructions in ring theory. In this paper, we study transfer of the AC property along local homomorphisms of Cohen-Macaulay rings. In particular, we show that the AC property is preserved by standard procedures in local algebra. Our results also yield new examples of Cohen-Macaulay AC rings.
AB - A 2003 counterexample to a conjecture of Auslander brought attention to a family of rings-colloquially called AC rings-that satisfy a natural condition on vanishing of cohomology. Several results attest to the remarkable homological properties of AC rings, but their definition is barely operational, and it remains unknown if they form a class that is closed under typical constructions in ring theory. In this paper, we study transfer of the AC property along local homomorphisms of Cohen-Macaulay rings. In particular, we show that the AC property is preserved by standard procedures in local algebra. Our results also yield new examples of Cohen-Macaulay AC rings.
UR - http://www.scopus.com/inward/record.url?scp=84866993888&partnerID=8YFLogxK
U2 - 10.1007/s00229-012-0540-7
DO - 10.1007/s00229-012-0540-7
M3 - Article
AN - SCOPUS:84866993888
SN - 0025-2611
VL - 139
SP - 535
EP - 544
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
IS - 3-4
ER -