1. Determining the primes of bad reduction of CM curves of genus 3
- Author
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Ionica, Sorina, Kiliçer, Pinar, Lauter, Kristin, García, Elisa Lorenzo, Mânzăţeanu, Adelina, Vincent, Christelle, Modélisation, Information et Systèmes - UR UPJV 4290 (MIS), Université de Picardie Jules Verne (UPJV), Universiteit Leiden, University of California [San Diego] (UC San Diego), University of California (UC), 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), Université de Neuchâtel (UNINE), and University of Vermont [Burlington]
- Subjects
Mathematics - Number Theory ,FOS: Mathematics ,Number Theory (math.NT) ,[MATH]Mathematics [math] - Abstract
In this paper we introduce a new problem called the Isogenous Embedding Problem (IEP). The existence of solutions to this problem is related to the primes of bad reduction of CM curves of genus $3$ and we can detect potentially good reduction in absence of solutions. We propose an algorithm for computing the solutions to the IEP and run the algorithm through different families of curves. We were able to prove the reduction type of some particular curves at certain primes that were open cases in [LLLR21].
- Published
- 2023