Rings with Auslander Dualizing Complexes

Details Rings with Auslander Dualizing Complexes Rings with Auslander Dualizing Complexes

1998-04-02

arxiv.org/abs/math/9804005v3

Mathematics

Rings and Algebras

39 pages, AMSLaTex. Final version, to appear in J. Algebra. Corrected mistake in proof of Thm. 1.13. minor corrections

Scientific paper

A ring with an Auslander dualizing complex is a generalization of an Auslander-Gorenstein ring. We show that many results which hold for Auslander-Gorenstein rings also hold in the more general setting. On the other hand we give criteria for existence of Auslander dualizing complexes which show these occur quite frequently. The most powerful tool we use is the Local Duality Theorem for connected graded algebras over a field. Filtrations allow the transfer of results to non-graded algebras. We also prove some results of a categorical nature, most notably the functoriality of rigid dualizing complexes.

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