• Counterexamples to the Hasse P...

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

Title:
Counterexamples to the Hasse Principle among the twists of the Klein quartic
Authors:
Elisa Lorenzo García, Michaël Vullers
Contributors:
Lorenzo García, Elisa, Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut de Mathématiques (UNINE), Université de Neuchâtel = University of Neuchatel (UNINE), ANR-20-CE40-0013,MELODIA,Méthodes pour les variétés abéliennes de petite dimension(2020)
Source:
Indagationes Mathematicae. 35:638-645
Publication Status:
Preprint
Publisher Information:
Elsevier BV, 2024.
Publication Year:
2024
Subject Terms:
Mathematics - Number Theory, FOS: Mathematics, 06 humanities and the arts, Number Theory (math.NT), 0101 mathematics, 01 natural sciences, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], 0604 arts, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
Document Type:
Fachzeitschrift Article
File Description:
application/pdf
Language:
English
ISSN:
0019-3577
DOI:
10.1016/j.indag.2023.08.007
DOI:
10.48550/arxiv.2212.10900
Access URL:
http://arxiv.org/abs/2212.10900
https://hal.science/hal-03915159v1/document
https://doi.org/10.1016/j.indag.2023.08.007
https://hal.science/hal-03915159v1
Rights:
CC BY
Accession Number:
edsair.doi.dedup.....5280a2e9d47a7575a73e3ed8b341655c
Database:
OpenAIRE

Weitere Informationen

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 at counter-examples to the Hasse principle.