Examples of effectivity for integral points on certain curves of genus 2

Fuente: arXiv
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Main Authors: Corvaja, Pietro, Lombardo, Davide, Zannier, Umberto
Format: Preprint
Published: 2024
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_version_ 1866913628543778816
author Corvaja, Pietro
Lombardo, Davide
Zannier, Umberto
author_facet Corvaja, Pietro
Lombardo, Davide
Zannier, Umberto
contents We consider families of smooth projective curves of genus 2 with a single point removed and study their integral points. We show that in many such families there is a dense set of fibres for which the integral points can be effectively determined. Our method is based on the construction of degree-3 étale covers of such curves of genus 2 and the study of the torsion values of sections of certain doubly elliptic abelian schemes.
format Preprint
id arxiv_https___arxiv_org_abs_2411_17930
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Examples of effectivity for integral points on certain curves of genus 2
Corvaja, Pietro
Lombardo, Davide
Zannier, Umberto
Number Theory
Algebraic Geometry
11D99, 11G30, 14G05
We consider families of smooth projective curves of genus 2 with a single point removed and study their integral points. We show that in many such families there is a dense set of fibres for which the integral points can be effectively determined. Our method is based on the construction of degree-3 étale covers of such curves of genus 2 and the study of the torsion values of sections of certain doubly elliptic abelian schemes.
title Examples of effectivity for integral points on certain curves of genus 2
topic Number Theory
Algebraic Geometry
11D99, 11G30, 14G05
url https://arxiv.org/abs/2411.17930