The integral Hasse principle for stacky curves associated to a family of generalized Fermat equations

2025/09/16 by Juanita Duque-Rosero, Christopher Keyes, Duque-Rosero, Juanita +9
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Topological and Geometric Data Analysis #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2509.13248

Abstract

We characterize the integral Hasse principle for an infinite family of spherical stacky curves with genus g∈ [2/3,1) that are defined using generalized Fermat equations, extending a result of Darmon and Granville. We then apply our methods to find that a positive proportion of curves in our family satisfy the integral Hasse principle.

Citations

• A guide to Tauberian theorems for arithmetic applications
• Local solubility of generalised Fermat equations
• The Brauer-Manin obstruction for stacky curves
• The local-global principle for integral points on stacky curves
• A Topology on Points on Stacks
• Artin-Schreier Root Stacks
• Fibrations with few rational points

Related

• Generalized Mordell curves, generalized Fermat curves, and the Hasse\n principle
• Algebraic families of hyperelliptic curves violating the Hasse principle
• An analytic viewpoint on the Hasse principle
• Contre-exemples au principe de Hasse pour les courbes de Fermat
• The Brauer-Manin obstruction for stacky curves