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
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.
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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)