PreprintCC BY 4.0arXiv
A cubic Chabauty criterion for hyperelliptic curves
Abstract
We establish a criterion for finiteness of the depth 3 Chabauty--Kim set X(ℚ2)3 for hyperelliptic curves X over ℚ with a rational Weierstrass point. To illustrate its applicability, we include an example of a genus $2$ curve satisfying the criterion whose Jacobian has Néron--Severi rank $1$ and Mordell--Weil rank $4$.
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BibTeX
@misc{berry2026cubic,
title = {{A cubic Chabauty criterion for hyperelliptic curves}},
author = {Lee Berry},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03255},
eprint = {2610.03255},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03255},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A cubic Chabauty criterion for hyperelliptic curves
AU - Lee Berry
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03255
UR - https://arxiv.org/abs/2610.03255
AB - We establish a criterion for finiteness of the depth 3 Chabauty--Kim set X(ℚ_2)_3 for hyperelliptic curves X over ℚ with a rational Weierstrass point. To illustrate its applicability, we include an example of a genus $2$ curve satisfying the criterion whose Jacobian has Néron--Severi rank $1$ and Mordell--Weil rank $4$.
ER -