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Semi-dualizing complexes and their Auslander categories


Author: Lars Winther Christensen
Journal: Trans. Amer. Math. Soc. 353 (2001), 1839-1883
MSC (1991): Primary 13D25, 13C15; Secondary 13D05, 13H10
DOI: https://doi.org/10.1090/S0002-9947-01-02627-7
Published electronically: January 4, 2001
MathSciNet review: 1813596
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Abstract: Let $R$ be a commutative Noetherian ring. We study $R$-modules, and complexes of such, with excellent duality properties. While their common properties are strong enough to admit a rich theory, we count among them such, potentially, diverse objects as dualizing complexes for $R$ on one side, and on the other, the ring itself. In several ways, these two examples constitute the extremes, and their well-understood properties serve as guidelines for our study; however, also the employment, in recent studies of ring homomorphisms, of complexes ``lying between'' these extremes is incentive.


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Additional Information

Lars Winther Christensen
Affiliation: Matematisk Afdeling, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark.
Email: winther@math.ku.dk

DOI: https://doi.org/10.1090/S0002-9947-01-02627-7
Received by editor(s): January 10, 1999
Received by editor(s) in revised form: March 9, 1999
Published electronically: January 4, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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