ON THE AUSLANDER-REITEN CONJECTURE FOR COHEN MACAULAY LOCAL RINGS

被引：14
|
作者：
Goto, Shiro [1 ]
Takahashi, Ryo [2 ]
机构：
[1] Meiji Univ, Sch Sci & Technol, Dept Math, Tama Ku, 1-1-1 Higashi Mita, Kawasaki, Kanagawa 2148571, Japan
[2] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 145卷 / 08期
关键词：
Auslander-Reiten conjecture; Tachikawa conjecture; Gorenstein ring; Cohen-Macaulay ring; semidualizing module;
D O I：
10.1090/proc/13487
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper studies vanishing of Ext modules over Cohen-Macaulay local rings. The main result of this paper implies that the Auslander-Reiten conjecture holds for maximal Cohen-Macaulay modules of rank one over Cohen-Macaulay normal local rings. It also recovers a theorem of Avramov-Buchweitz-S, ega and Hanes-Huneke, which shows that the Tachikawa conjecture holds for Cohen-Macaulay generically Gorenstein local rings.
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页码：3289 / 3296
页数：8
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