斜率有界性和等分布定理

IF 0.9 2区数学 Q2 MATHEMATICS

International Mathematics Research Notices Pub Date : 2024-04-05 DOI:10.1093/imrn/rnae057

Wenbin Luo

{"title":"斜率有界性和等分布定理","authors":"Wenbin Luo","doi":"10.1093/imrn/rnae057","DOIUrl":null,"url":null,"abstract":"In this article, we prove the boundedness of minimal slopes of adelic line bundles over function fields of characteristic $0$. This can be applied to prove the equidistribution of generic and small points with respect to a big and semipositive adelic line bundle. Our methods can be applied to the finite places of number fields as well. We also show the continuity of $\\chi $-volumes over function fields.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":"1 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Slope Boundedness and Equidistribution Theorem\",\"authors\":\"Wenbin Luo\",\"doi\":\"10.1093/imrn/rnae057\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we prove the boundedness of minimal slopes of adelic line bundles over function fields of characteristic $0$. This can be applied to prove the equidistribution of generic and small points with respect to a big and semipositive adelic line bundle. Our methods can be applied to the finite places of number fields as well. We also show the continuity of $\\\\chi $-volumes over function fields.\",\"PeriodicalId\":14461,\"journal\":{\"name\":\"International Mathematics Research Notices\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-04-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Mathematics Research Notices\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1093/imrn/rnae057\",\"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":"International Mathematics Research Notices","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/imrn/rnae057","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

在本文中，我们证明了特征 $0$ 的函数域上的阿德尔线束的最小斜率的有界性。这可用于证明关于大且半正的 adelic 线束的一般点和小点的等分布。我们的方法也可以应用于数域的有限位置。我们还证明了函数场上$chi$卷的连续性。

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

Slope Boundedness and Equidistribution Theorem

In this article, we prove the boundedness of minimal slopes of adelic line bundles over function fields of characteristic $0$. This can be applied to prove the equidistribution of generic and small points with respect to a big and semipositive adelic line bundle. Our methods can be applied to the finite places of number fields as well. We also show the continuity of $\chi $-volumes over function fields.

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

International Mathematics Research Notices 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

316

审稿时长

1 months

期刊介绍： International Mathematics Research Notices provides very fast publication of research articles of high current interest in all areas of mathematics. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics.