克莱因四次方畸变中的哈塞原理反例

Pub Date : 2024-07-01 DOI:10.1016/j.indag.2023.08.007
Elisa Lorenzo García , Michaël Vullers
{"title":"克莱因四次方畸变中的哈塞原理反例","authors":"Elisa Lorenzo García ,&nbsp;Michaël Vullers","doi":"10.1016/j.indag.2023.08.007","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we inspect from closer the local and global points of the twists of the Klein quartic. For the local ones we use geometric arguments, while for the global ones we strongly use the modular interpretation of the twists. The main result is providing families with (conjecturally infinitely many) twists of the Klein quartic that are counterexamples to the Hasse Principle.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0019357723000848/pdfft?md5=03e46a5dbb56004e38e7926d976cb7c3&pid=1-s2.0-S0019357723000848-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Counterexamples to the Hasse Principle among the twists of the Klein quartic\",\"authors\":\"Elisa Lorenzo García ,&nbsp;Michaël Vullers\",\"doi\":\"10.1016/j.indag.2023.08.007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper we inspect from closer the local and global points of the twists of the Klein quartic. For the local ones we use geometric arguments, while for the global ones we strongly use the modular interpretation of the twists. The main result is providing families with (conjecturally infinitely many) twists of the Klein quartic that are counterexamples to the Hasse Principle.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0019357723000848/pdfft?md5=03e46a5dbb56004e38e7926d976cb7c3&pid=1-s2.0-S0019357723000848-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0019357723000848\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019357723000848","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

在本文中,我们从近处考察了克莱因四次方捻的局部和全局点。对于局部点,我们使用了几何论证,而对于全局点,我们则大力使用了捻的模块解释。本文的主要成果是提供了克莱因四次方捻线的(猜想中无限多的)族,这些族是哈塞原理的反例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
分享
查看原文
Counterexamples to the Hasse Principle among the twists of the Klein quartic

In this paper we inspect from closer the local and global points of the twists of the Klein quartic. For the local ones we use geometric arguments, while for the global ones we strongly use the modular interpretation of the twists. The main result is providing families with (conjecturally infinitely many) twists of the Klein quartic that are counterexamples to the Hasse Principle.

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
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信