, Volume 230, Issue 3, pp 545-567

Depth for complexes, and intersection theorems

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This paper introduces a new notion of depth for complexes; it agrees with the classical definition for modules, and coincides with earlier extensions to complexes, whenever those are defined. Techniques are developed leading to a quick proof of an extension of the Improved New Intersection Theorem (this uses Hochster's big Cohen-Macaulay modules), and also a generalization of the “depth formula” for tensor product of modules. Properties of depth for complexes are established, extending the usual properties of depth for modules.

Received May 6, 1997; in final form December 3, 1997