1998/04/02 by Amnon Yekutieli, Yekutieli, Amnon, James J. Zhang +1
Mathematics · #16D90 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16D90
paper · pdf · doi:10.48550/arxiv.math/9804005
39 pages, AMSLaTex. Final version, to appear in J. Algebra. Corrected mistake in proof of Thm. 1.13. minor corrections
openalex publication_date 1998/04/02 · arxiv created 1998/09/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.