Counterexamples to the Hasse Principle among the twists of the Klein quartic

被引：0

作者：

Garcia, Elisa Lorenzo ^{[1
,2
]}

Vullers, Michael ^{[3
]}

机构：

[1] Univ Neuchatel, Inst Math, Rue Emile Argand 11, CH-2000 Neuchatel, Switzerland

[2] Univ Rennes 1, Lab IRMAR, Off 602,Campus Beaulieu, F-35042 Rennes, France

[3] IT Monitoring Engineer TenneT TSOBV, Arnhem, Netherlands

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2024年 / 35卷 / 04期

关键词：

Local-global principle; Modular curves; Twists; CURVES;

D O I：

10.1016/j.indag.2023.08.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (c) 2023 The Author(s). Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG). This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

引用

页码：638 / 645

页数：8

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