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DUALIZING DIFFERENTIAL GRADED MODULES AND GORENSTEIN DIFFERENTIAL GRADED ALGEBRAS

Published online by Cambridge University Press:  25 September 2003

ANDERS FRANKILD ,
SRIKANTH IYENGAR  and
PETER JØRGENSEN
ANDERS FRANKILD
Affiliation:
Matematisk Afdeling, Københavns Universitet, Kø-benhavn Ø, Denmarkfrankild@math.ku.dk
SRIKANTH IYENGAR
Affiliation:
Mathematics Department, University of Missouri, Columbia, MO 65211, USAiyengar@math.missouri.edu
PETER JØRGENSEN
Affiliation:
Danish National Library of Science and Medicine, Nørre Allé 49, 2200 Kø-benhavn N, Denmarkpej@dnlb.dk
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Abstract

The paper explores dualizing differential graded (DG) modules over DG algebras. The focus is on DG algebras that are commutative local, and finite. One of the main results established is that, for this class of DG algebras, a finite DG module is dualizing precisely when its Bass number is 1. As a corollary, one obtains that the Avramov–Foxby notion of Gorenstein DG algebras coincides with that due to Frankild and Jørgensen. One other key result is that, under suitable hypotheses, any two dualizing DG modules are quasiisomorphic up to a suspension. In addition, it is established that a number of naturally occurring DG algebras possess dualizing DG modules.

Keywords

13D9913H1016E45
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 2 , October 2003 , pp. 288 - 306
Copyright
The London Mathematical Society 2003

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