arxiv:2401.05228

Local heights on hyperelliptic curves and quadratic Chabauty

Published on Jan 10, 2024

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Abstract

An algorithm is presented to compute local heights for hyperelliptic curves, enhancing the applicability of the quadratic Chabauty method to curves with non-trivial local heights.

AI-generated summary

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 ellneq 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.

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