Explicit height estimates for CM curves of genus 2

2023/11/22 by Linda Frey, Frey, Linda, Samuel Le Fourn +3
Mathematics · Social Sciences · #11G15 #11G30 #11L07 #11R29 #11R42 #11Y40 #14G50 #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.2311.13403

openalex publication_date 2023/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper we make explicit the constants of Habegger and Pazuki's work from 2017 on bounding the discriminant of cyclic Galois CM fields corresponding to genus 2 curves with CM by them and potentially good reduction outside a predefined set of primes. We also simplify some of the arguments.

Related

• A bound on the primes of bad reduction for CM curves of genus 3
• Cyclic Cubic Points on Higher Genus Curves
• The CM class number one problem for curves of genus 2
• Heights of CM cycles and derivatives of L-series
• Reduction types of CM curves