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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/16681

Title: The Homological Theory of Maximal Cohen-Macaulay Approximations
Authors: Auslander, Maurice
Buchweitz, Ragnar-Olaf
Issue Date: 1989
Publisher: Paris: Gauthier-Villars
Citation: Societe Mathematique de France Memoire, v. 38, pgs 5-37
Abstract: Let R be a commutative noetherian Cohen-Macaulay ring which admits a dualizing module. We show that for any finitely generated R-module N there exists a maximal Cohen-Macaulay R-module M which surjects onto N and such that any other surjection from a maximal Cohen-Macaulay module onto N factors over it. Dually, there is a finitely generated R-module I of finite injective dimension into which N embeds, universal for such embeddings. We prove and investigate these results in the broader context of abellan categories with a suitable subcategory of "maximal Cohen-Macaulay objects" extracting for this purpose those ingredients of Grothendieck-Serre duality theory which are needed.
URI: http://hdl.handle.net/1807/16681
Appears in Collections:Mathematics

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