Local heights on hyperelliptic curves and quadratic Chabauty

Transactions of the American Mathematical Society Series B 2026 Open access

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Authors: L. Alexander Betts, Juanita Duque-Rosero, Sachi Hashimoto, Pim Spelier
DOI: 10.1090/btran/242
Cited by: 0

Abstract

Local heights are arithmetic invariants used in the quadratic Chabauty method for determining the rational points on curves. We present an algorithm to compute these local heights for hyperelliptic curves at odd primes ℓ ≠ p \ell \neq p . This algorithm significantly broadens the applicability of quadratic Chabauty to curves which were previously inaccessible due to the presence of non-trivial local heights. We provide numerous examples, including the first quadratic Chabauty computation for a curve having two primes with non-trivial local heights.

Fields of Study & Subjects

Advanced Numerical Analysis Techniques Algebraic Geometry and Number Theory Cryptography and Residue Arithmetic

Publication details

Journal / source
Transactions of the American Mathematical Society Series B
Volume
13
Issue
8
Pages
240–300
Publication date
22 April 2026
Language
EN