Semi-dualizing complexes and their Auslander categories

Christensen, Lars

doi:10.1090/S0002-9947-01-02627-7

Semi-dualizing complexes and their Auslander categories
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by Lars Winther Christensen PDF

Trans. Amer. Math. Soc. 353 (2001), 1839-1883 Request permission

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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