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Rings with Auslander Dualizing Complexes

โœ Scribed by Amnon Yekutieli; James J. Zhang

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
305 KB
Volume
213
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

A ring with an Auslander dualizing complex is a generalization of an Auslan-derแŽGorenstein ring. We show that many results which hold for AuslanderแŽ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 nongraded algebras. We also prove some results of a categorical nature, most notably the functoriality of rigid dualizing complexes. แฎŠ 1999 Academic Press Contents.

0. Introduction.

  1. Dualizing complexes.

2. Auslander dualizing complexes.

  1. Rigid dualizing complexes.

4. Dualizing complexes oยจer graded algebras.

  1. Graded algebras with some commutatiยจity hypothesis.

  2. Noetherian connected filtrations.

๐Ÿ“œ SIMILAR VOLUMES

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## Abstract Let __A__ be a commutative Noetherian local ring satisfying the approximation property. This means that any system of polynomial equations over __A__ having a solution in the completion ว has also a solution in __A.__ Then __A__ is proven to admit a dualizing complex.