Determining the primes of bad reduction of cm curves of genus 3
KILIÇER, Pınar
Lithe and fast algorithmic number theory [LFANT]
Universiteit Leiden = Leiden University
Analyse cryptographique et arithmétique [CANARI]
Lithe and fast algorithmic number theory [LFANT]
Universiteit Leiden = Leiden University
Analyse cryptographique et arithmétique [CANARI]
LAUTER, Kristin
Université de Neuchâtel = University of Neuchatel [UNINE]
Modélisation, Information et Systèmes - UR UPJV 4290 [MIS]
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Université de Neuchâtel = University of Neuchatel [UNINE]
Modélisation, Information et Systèmes - UR UPJV 4290 [MIS]
KILIÇER, Pınar
Lithe and fast algorithmic number theory [LFANT]
Universiteit Leiden = Leiden University
Analyse cryptographique et arithmétique [CANARI]
Lithe and fast algorithmic number theory [LFANT]
Universiteit Leiden = Leiden University
Analyse cryptographique et arithmétique [CANARI]
LAUTER, Kristin
Université de Neuchâtel = University of Neuchatel [UNINE]
Modélisation, Information et Systèmes - UR UPJV 4290 [MIS]
Université de Neuchâtel = University of Neuchatel [UNINE]
Modélisation, Information et Systèmes - UR UPJV 4290 [MIS]
LORENZO GARCÍA, Elisa
Institut de Recherche Mathématique de Rennes [IRMAR]
Modélisation, Information et Systèmes - UR UPJV 4290 [MIS]
Institut de Recherche Mathématique de Rennes [IRMAR]
Modélisation, Information et Systèmes - UR UPJV 4290 [MIS]
MÂNZĂŢEANU, Adelina
Universiteit Leiden = Leiden University
Modélisation, Information et Systèmes - UR UPJV 4290 [MIS]
Universiteit Leiden = Leiden University
Modélisation, Information et Systèmes - UR UPJV 4290 [MIS]
VINCENT, Christelle
University of Vermont [Burlington]
Modélisation, Information et Systèmes - UR UPJV 4290 [MIS]
< Reduce
University of Vermont [Burlington]
Modélisation, Information et Systèmes - UR UPJV 4290 [MIS]
Language
en
Article de revue
This item was published in
Quarterly Journal of Mathematics. 2024-03-05
Oxford University Press (OUP)
English Abstract
In this paper, we introduce a new problem called the Isogenous Embedding Problem (IEP) and relate the existence of solutions to this problem to the primes of bad reduction of complex multiplication curves of genus 3. More ...Read more >
In this paper, we introduce a new problem called the Isogenous Embedding Problem (IEP) and relate the existence of solutions to this problem to the primes of bad reduction of complex multiplication curves of genus 3. More precisely, the absence of solutions to IEP implies potentially good reduction. We propose an algorithm for computing the solutions to the IEP and run the algorithm through different families of curves. Using this algorithm, we were able to prove the reduction type of some particular curves at certain primes that were open cases in R. Lercier, Q. Liu, E. Lorenzo García and C. Ritzenthaler, Reduction type of smooth plane quartics, Algebra Number Theory 15 no. 6 2021, 1429–1468.Read less <
ANR Project
Méthodes pour les variétés abéliennes de petite dimension - ANR-20-CE40-0013
Origin
Hal imported