平面仿射群方案的平面性和同态的纤维判据

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI:10.1016/j.jpaa.2025.107949

Phùng Hô Hai , Hop D. Nguyen , João Pedro dos Santos

{"title":"平面仿射群方案的平面性和同态的纤维判据","authors":"Phùng Hô Hai , Hop D. Nguyen , João Pedro dos Santos","doi":"10.1016/j.jpaa.2025.107949","DOIUrl":null,"url":null,"abstract":"<div><div>A very useful result concerning flatness in Algebraic Geometry is EGA's “fiber” criterion. We propose similar fiber criteria to verify flatness of a module while avoiding “finiteness” assumptions. Motivated by a Tannakian viewpoint (where the category of representations comes to the front), we derive applications to the theory of affine and flat group schemes.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107949"},"PeriodicalIF":0.7000,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fiber criteria for flatness and homomorphisms of flat affine group schemes\",\"authors\":\"Phùng Hô Hai , Hop D. Nguyen , João Pedro dos Santos\",\"doi\":\"10.1016/j.jpaa.2025.107949\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>A very useful result concerning flatness in Algebraic Geometry is EGA's “fiber” criterion. We propose similar fiber criteria to verify flatness of a module while avoiding “finiteness” assumptions. Motivated by a Tannakian viewpoint (where the category of representations comes to the front), we derive applications to the theory of affine and flat group schemes.</div></div>\",\"PeriodicalId\":54770,\"journal\":{\"name\":\"Journal of Pure and Applied Algebra\",\"volume\":\"229 6\",\"pages\":\"Article 107949\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-03-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Pure and Applied Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S002240492500088X\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pure and Applied Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002240492500088X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

代数几何中关于平面性的一个非常有用的结果是EGA的“纤维”判据。我们提出了类似的纤维标准来验证模块的平整度，同时避免了“有限”假设。在Tannakian观点的激励下（表示的范畴出现在前面），我们推导了仿射和平面群方案理论的应用。

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

Fiber criteria for flatness and homomorphisms of flat affine group schemes

A very useful result concerning flatness in Algebraic Geometry is EGA's “fiber” criterion. We propose similar fiber criteria to verify flatness of a module while avoiding “finiteness” assumptions. Motivated by a Tannakian viewpoint (where the category of representations comes to the front), we derive applications to the theory of affine and flat group schemes.

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

Journal of Pure and Applied Algebra 数学-数学

CiteScore

1.70

自引率

12.50%

发文量

225

审稿时长

17 days

期刊介绍： The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.