{"title":"用Brauer类丰富了算术曲面的最小模型程序","authors":"Daniel Chan , Colin Ingalls","doi":"10.1016/j.jalgebra.2025.03.047","DOIUrl":null,"url":null,"abstract":"<div><div>We examine the noncommutative minimal model program for orders on arithmetic surfaces, or equivalently, arithmetic surfaces enriched by a Brauer class <em>β</em>. When <em>β</em> has prime index <span><math><mi>p</mi><mo>></mo><mn>5</mn></math></span>, we show the classical theory extends with analogues of existence of terminal resolutions, Castelnuovo contraction and Zariski factorisation. We also classify <em>β</em>-terminal surfaces and Castelnuovo contractions, and discover new unexpected behaviour.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"676 ","pages":"Pages 475-511"},"PeriodicalIF":0.8000,"publicationDate":"2025-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The minimal model program for arithmetic surfaces enriched by a Brauer class\",\"authors\":\"Daniel Chan , Colin Ingalls\",\"doi\":\"10.1016/j.jalgebra.2025.03.047\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We examine the noncommutative minimal model program for orders on arithmetic surfaces, or equivalently, arithmetic surfaces enriched by a Brauer class <em>β</em>. When <em>β</em> has prime index <span><math><mi>p</mi><mo>></mo><mn>5</mn></math></span>, we show the classical theory extends with analogues of existence of terminal resolutions, Castelnuovo contraction and Zariski factorisation. We also classify <em>β</em>-terminal surfaces and Castelnuovo contractions, and discover new unexpected behaviour.</div></div>\",\"PeriodicalId\":14888,\"journal\":{\"name\":\"Journal of Algebra\",\"volume\":\"676 \",\"pages\":\"Pages 475-511\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-08-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021869325002108\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/4/15 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869325002108","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/4/15 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
The minimal model program for arithmetic surfaces enriched by a Brauer class
We examine the noncommutative minimal model program for orders on arithmetic surfaces, or equivalently, arithmetic surfaces enriched by a Brauer class β. When β has prime index , we show the classical theory extends with analogues of existence of terminal resolutions, Castelnuovo contraction and Zariski factorisation. We also classify β-terminal surfaces and Castelnuovo contractions, and discover new unexpected behaviour.
期刊介绍：
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.
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