Effective Mordell for curves with enough automorphisms

2025/03/13 by Garcia-Fritz, Natalia, Pasten, Hector · 1 citation
#11G50 #FOS: Mathematics #Number Theory (math.NT) #Primary: 14G05 #Secondary: 14G40

paper · doi:10.48550/arxiv.2503.10443

Abstract

We prove a completely explicit and effective upper bound for the Néron--Tate height of rational points of curves of genus at least 2 over number fields, provided that they have enough automorphisms with respect to the Mordell--Weil rank of their jacobian. Our arguments build on Arakelov theory for arithmetic surfaces. Our bounds are practical, and we illustrate this by explicitly computing the rational points of a certain genus 2 curve whose jacobian has Mordell--Weil rank 2.

Cited by

• Effective height bounds via Mordell Weil lattice symmetries

Related

• Effective height bounds via Mordell Weil lattice symmetries
• Uniformity in Mordell-Lang for curves
• Ranks of rational points of the Jacobian varieties of hyperelliptic curves
• The explicit Mordell Conjecture for families of curves (with an appendix by M. Stoll)
• Explicit height bounds and the explicit Mordell-Lang Conjecture