On the structure of Cohen-Macaulay modules over hypersurfaces of countable Cohen-Macaulay representation type

被引：11

作者：

Araya, Tokuji ^{[4
]}

Iima, Kei-ichiro ^{[2
]}

Takahashi, Ryo ^{[1
,3
]}

机构：

[1] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

[2] Nara Natl Coll Technol, Dept Liberal Studies, Yamato Koriyama, Nara 6391080, Japan

[3] Shinshu Univ, Fac Sci, Dept Math Sci, Matsumoto, Nagano 3908621, Japan

[4] Nara Univ Educ, Takabatake, Nara 6308528, Japan

来源：

JOURNAL OF ALGEBRA | 2012年 / 361卷

关键词：

Hypersurface; Maximal Cohen-Macaulay module; Countable Cohen-Macaulay representation type; Stable category; Knorrer's periodicity; SINGULARITIES; SUBCATEGORIES;

D O I：

10.1016/j.jalgebra.2012.03.032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a complete local hypersurface over an algebraically closed field of characteristic different from two, and suppose that R has countable Cohen-Macaulay (CM) representation type. In this paper, it is proved that the maximal Cohen-Macaulay (MCM) R-modules which are locally free on the punctured spectrum are dominated by the MCM R-modules which are not locally free on the punctured spectrum. More precisely, there exists a single R-module X such that the indecomposable MCM R-modules not locally free on the punctured spectrum are X and its syzygy Omega X and that any other MCM R-modules are obtained from extensions of X and Omega X. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：213 / 224

页数：12

共 11 条

[1]

[Anonymous], 1995, CAMBRIDGE STUD ADV M

[2] COHEN-MACAULAY MODULES ON HYPERSURFACE SINGULARITIES .2. [J].