Maximal Cohen–Macaulay Modules and Gorenstein Algebras

✍ Scribed by Jan O Kleppe; Chris Peterson

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 174 KB
• Volume: 238
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8665

✦ Synopsis

Let B be a graded Cohen᎐Macaulay quotient of a Gorenstein ring, R. It is known that sections of the dual of the canonical module, K , can be used to B construct Gorenstein quotients of R. The purpose of this paper is to place this method of construction into a broader context. If M is a maximal Cohen᎐Macaulay B-module whose sheafified top exterior power is a twist of K and if M satisfies B certain additional homological conditions then regular sections of M U can again be used to construct Gorenstein quotients of R. On Cohen᎐Macaulay quotients, the normal module, the first Koszul homology module and several other associated modules all have sheafified top exterior power equal to a twist of K . If additional B restrictions are placed on the Cohen᎐Macaulay quotients then these modules will satisfy the required additional homological conditions. This places the canonical module within a broad family of easily manipulated maximal Cohen᎐Macaulay modules whose sections can be used to construct Gorenstein quotients of R.