TY - JOUR

T1 - A test complex for gorensteinness

AU - Christensen, Lars Winther

AU - Veliche, Oana

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2008/2

Y1 - 2008/2

N2 - Let R be a commutative noetherian ring with a dualizing complex. By recent work of Iyengar and Krause (2006), the difference between the category of acyclic complexes and its subcategory of totally acyclic complexes measures how far R is from being Gorenstein. In particular, R is Gorenstein if and only if every acyclic complex is totally acyclic. In this note we exhibit a specific acyclic complex with the property that it is totally acyclic if and only if R is Gorenstein.

AB - Let R be a commutative noetherian ring with a dualizing complex. By recent work of Iyengar and Krause (2006), the difference between the category of acyclic complexes and its subcategory of totally acyclic complexes measures how far R is from being Gorenstein. In particular, R is Gorenstein if and only if every acyclic complex is totally acyclic. In this note we exhibit a specific acyclic complex with the property that it is totally acyclic if and only if R is Gorenstein.

UR - http://www.scopus.com/inward/record.url?scp=70349652403&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-07-09129-0

DO - 10.1090/S0002-9939-07-09129-0

M3 - Article

AN - SCOPUS:70349652403

VL - 136

SP - 479

EP - 487

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -