The local-global principle for integral points on stacky curves

2020/05/30 by Bhargava, Manjul, Poonen, Bjorn · 1 citation
#11G30 (Primary) 14A20 #14G25 #14H25 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2006.00167

Abstract

We construct a stacky curve of genus 1/2 (i.e., Euler characteristic 1) over ℤ that has an ℝ-point and a ℤ_p-point for every prime p but no ℤ-point. This is best possible: we also prove that any stacky curve of genus less than 1/2 over a ring of S-integers of a global field satisfies the local-global principle for integral points.

Cited by

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

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