代数曲面上的中心扩展与Riemann-Roch定理

IF 0.8 4区数学 Q2 MATHEMATICS

Sbornik Mathematics Pub Date : 2021-05-30 DOI:10.1070/SM9623

D. Osipov

{"title":"代数曲面上的中心扩展与Riemann-Roch定理","authors":"D. Osipov","doi":"10.1070/SM9623","DOIUrl":null,"url":null,"abstract":"We study canonical central extensions of the general linear group over the ring of adeles on a smooth projective algebraic surface X by means of the group of integers. By these central extensions and adelic transition matrices of a rank n locally free sheaf of O X -modules we obtain the local (adelic) decomposition for the diﬀerence of Euler characteristics of this sheaf and the sheaf O nX . Two various calculations of this diﬀerence lead to the Riemann-Roch theorem on X (without the Noether formula).","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2021-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Central extensions and Riemann-Roch theorem on algebraic surfaces\",\"authors\":\"D. Osipov\",\"doi\":\"10.1070/SM9623\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study canonical central extensions of the general linear group over the ring of adeles on a smooth projective algebraic surface X by means of the group of integers. By these central extensions and adelic transition matrices of a rank n locally free sheaf of O X -modules we obtain the local (adelic) decomposition for the diﬀerence of Euler characteristics of this sheaf and the sheaf O nX . Two various calculations of this diﬀerence lead to the Riemann-Roch theorem on X (without the Noether formula).\",\"PeriodicalId\":49573,\"journal\":{\"name\":\"Sbornik Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-05-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Sbornik Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1070/SM9623\",\"RegionNum\":4,\"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":"Sbornik Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1070/SM9623","RegionNum":4,"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

利用整数群研究了光滑射影代数曲面X上阿德尔环上一般线性群的正则中心扩展。通过这些中心扩展和O X -模的n阶局部自由层的阿德利转移矩阵，我们得到了该层与O nX层欧拉特性差异的局部(阿德利)分解。对这种差异的两种不同的计算得出了关于X的黎曼-洛克定理(没有诺特公式)。

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

Central extensions and Riemann-Roch theorem on algebraic surfaces

We study canonical central extensions of the general linear group over the ring of adeles on a smooth projective algebraic surface X by means of the group of integers. By these central extensions and adelic transition matrices of a rank n locally free sheaf of O X -modules we obtain the local (adelic) decomposition for the diﬀerence of Euler characteristics of this sheaf and the sheaf O nX . Two various calculations of this diﬀerence lead to the Riemann-Roch theorem on X (without the Noether formula).

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

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis