Title:
Rigid
Dualizing Complexes over Commutative Rings
Authors:
Amnon
Yekutieli and James J. Zhang
Publication
status:
Algebras
and Representation Theory
12,
Number 1 (2009), 19-52
Abstract:
In
this paper we present a new approach to Grothendieck duality over
commutative rings. Our approach is based on the idea of rigid
dualizing complexes, which was introduced by Van den Bergh in the
context of noncommutative algebraic geometry. The method of rigidity
was modied to work over general commutative base rings in our paper
[YZ5]. In the present paper we obtain many of the important local
features of Grothendieck duality, yet manage to avoid lengthy and
difficult compatibility verifications. Our results apply to
essentially finite type algebras over a regular noetherian finite
dimensional base ring, and hence are suitable for arithmetic rings.
In the sequel paper [Ye4] these results will be used to construct and
study rigid dualizing complexes on schemes.
Electronic
Preprint:
amslatex
file
pdf file (acrobat)
Warning. The paper "Rigid Complexes via DG Algebras" (referred to as [YZ5] above) has severe gaps in some of the proofs. It is possible that some of these problems spilled over to this paper. We are in the process of repairing these problems, and formal errata, and also corrected papers, should be available during 2015.
(updated 28 December 2014)