Geometric quadratic Chabauty and \(p\)-adic heights

DOI10.1016/j.exmath.2023.05.003arXiv2207.10389OpenAlexW4377107578MaRDI QIDQ6080386

Juanita Duque-Rosero, Pim Spelier, Sachi Hashimoto

Publication date: 2 October 2023

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.10389

zbMATH Keywords

rational pointshyperelliptic curvesbiextensions\(p\)-adic heightsChabauty's methodgeometric quadratic Chabauty

Mathematics Subject Classification ID

Rational points (14G05) Heights (11G50)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quadratic Chabauty: \(p\)-adic heights and integral points on hyperelliptic curves
• The unipotent Albanese map and Selmer varieties for curves
• Effective Chabauty
• Finiteness theorems for abelian varieties over number fields.
• Torsion des courbes elliptiques sur les corps cubiques. (Torsion of elliptic curves over cubic fields)
• A Macaulay2 package for computations with rational maps
• Quadratic Chabauty and rational points. I: \(p\)-adic heights
• Explicit Chabauty-Kim for the split Cartan modular curve of level 13
• On the theory of commutative formal groups
• \(p\)-adic heights and Vologodsky integration
• Computing Local p-adic Height Pairings on Hyperelliptic Curves
• Maps on Ultrametric Spaces, Hensel's Lemma, and Differential Equations Over Valued Fields
• Explicit endomorphisms and Correspondences
• Computing in the Jacobian of a Hyperelliptic Curve
• Linear algebra algorithms for divisors on an algebraic curve
• Rigorous computation of the endomorphism ring of a Jacobian
• Explicit Coleman Integration for Hyperelliptic Curves
• Two Recent p-adic Approaches Towards the (Effective) Mordell Conjecture
• A geometric linear Chabauty comparison theorem
• Quadratic Chabauty and Rational Points II: Generalised Height Functions on Selmer Varieties
• Hensel-lifting torsion points on Jacobians and Galois representations
• Explicit arithmetic intersection theory and computation of Néron-Tate heights
• GEOMETRIC QUADRATIC CHABAUTY
• Quadratic Chabauty for modular curves: algorithms and examples
• Weight filtrations on Selmer schemes and the effective Chabauty–Kim method
• Fast Jacobian arithmetic for hyperelliptic curves of genus 3

This page was built for publication: Geometric quadratic Chabauty and \(p\)-adic heights