Publication status: J. Algebra 213 (1999), 1-51.
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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