最大科恩-麦考莱模块类别的谱

arXiv - MATH - Commutative Algebra Pub Date : 2024-07-24 DOI:arxiv-2407.16913

Naoya Hiramatsu

{"title":"最大科恩-麦考莱模块类别的谱","authors":"Naoya Hiramatsu","doi":"arxiv-2407.16913","DOIUrl":null,"url":null,"abstract":"We introduce an analog of the Ziegler spectrum for maximal Cohen-Macaulay\nmodules over a complete Cohen-Macaulay local ring. We define a topology on the\nspace of isomorphism classes of indecomposable maximal Cohen-Macaulay modules\nand investigate the topological structure. We also calculate the\nCantor-Bendixson rank for a ring which is of CM_+-finite representation type.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"162 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The spectrum of a category of maximal Cohen-Macaulay modules\",\"authors\":\"Naoya Hiramatsu\",\"doi\":\"arxiv-2407.16913\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce an analog of the Ziegler spectrum for maximal Cohen-Macaulay\\nmodules over a complete Cohen-Macaulay local ring. We define a topology on the\\nspace of isomorphism classes of indecomposable maximal Cohen-Macaulay modules\\nand investigate the topological structure. We also calculate the\\nCantor-Bendixson rank for a ring which is of CM_+-finite representation type.\",\"PeriodicalId\":501475,\"journal\":{\"name\":\"arXiv - MATH - Commutative Algebra\",\"volume\":\"162 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Commutative Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.16913\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Commutative Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.16913","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们引入了完整科恩-麦考莱局部环上最大科恩-麦考莱模块的齐格勒谱。我们定义了不可分解最大 Cohen-Macaulay 模块同构类空间的拓扑结构，并研究了其拓扑结构。我们还计算了 CM_+ 有限表示类型的环的康托-本迪克森秩。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The spectrum of a category of maximal Cohen-Macaulay modules

We introduce an analog of the Ziegler spectrum for maximal Cohen-Macaulay modules over a complete Cohen-Macaulay local ring. We define a topology on the space of isomorphism classes of indecomposable maximal Cohen-Macaulay modules and investigate the topological structure. We also calculate the Cantor-Bendixson rank for a ring which is of CM_+-finite representation type.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Commutative Algebra

自引率

0.00%

发文量