大多数完全真实的场没有普遍形式或诺斯科特性质

IF 9.1 1区综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES

Proceedings of the National Academy of Sciences of the United States of America Pub Date : 2025-05-16 DOI:10.1073/pnas.2419414122

Nicolas Daans, Vítězslav Kala, Siu Hang Man, Martin Widmer, Pavlo Yatsyna

{"title":"大多数完全真实的场没有普遍形式或诺斯科特性质","authors":"Nicolas Daans, Vítězslav Kala, Siu Hang Man, Martin Widmer, Pavlo Yatsyna","doi":"10.1073/pnas.2419414122","DOIUrl":null,"url":null,"abstract":"We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott property, is meager. The main tool is a theorem on the number of square classes of totally positive units represented by a quadratic lattice of a given rank.","PeriodicalId":20548,"journal":{"name":"Proceedings of the National Academy of Sciences of the United States of America","volume":"4 1","pages":""},"PeriodicalIF":9.1000,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Most totally real fields do not have universal forms or the Northcott property\",\"authors\":\"Nicolas Daans, Vítězslav Kala, Siu Hang Man, Martin Widmer, Pavlo Yatsyna\",\"doi\":\"10.1073/pnas.2419414122\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott property, is meager. The main tool is a theorem on the number of square classes of totally positive units represented by a quadratic lattice of a given rank.\",\"PeriodicalId\":20548,\"journal\":{\"name\":\"Proceedings of the National Academy of Sciences of the United States of America\",\"volume\":\"4 1\",\"pages\":\"\"},\"PeriodicalIF\":9.1000,\"publicationDate\":\"2025-05-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the National Academy of Sciences of the United States of America\",\"FirstCategoryId\":\"103\",\"ListUrlMain\":\"https://doi.org/10.1073/pnas.2419414122\",\"RegionNum\":1,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the National Academy of Sciences of the United States of America","FirstCategoryId":"103","ListUrlMain":"https://doi.org/10.1073/pnas.2419414122","RegionNum":1,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}

引用次数: 0

摘要

我们证明了在具有可构造拓扑的全实数域的空间中，承认具有全称二次型或具有Northcott性质的域的集合是很少的。主要的工具是关于由给定秩的二次格表示的完全正单元的平方类的数目的定理。

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

Most totally real fields do not have universal forms or the Northcott property

We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott property, is meager. The main tool is a theorem on the number of square classes of totally positive units represented by a quadratic lattice of a given rank.

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

Proceedings of the National Academy of Sciences of the United States of America 综合性期刊-综合性期刊

CiteScore

19.00

自引率

0.90%

发文量

3575

审稿时长

2.5 months

期刊介绍： The Proceedings of the National Academy of Sciences (PNAS), a peer-reviewed journal of the National Academy of Sciences (NAS), serves as an authoritative source for high-impact, original research across the biological, physical, and social sciences. With a global scope, the journal welcomes submissions from researchers worldwide, making it an inclusive platform for advancing scientific knowledge.