PreprintCC BY 4.0arXiv
Explicit Coleman integration over finite extensions of ℚp
Abstract
Coleman integration is an important computational ingredient of the Chabauty--Coleman method and its extensions. We extend the Balakrishnan--Tuitman algorithm to general smooth projective curves with good reduction over arbitrary finite extensions of ℚp, allowing both ramification and nontrivial residue degree. Given a suitable plane model and integral bases, we provide explicit precision bounds and an accompanying Magma implementation. As an application, a single-prime computation at p=19 over the unramified quadratic extension ℚ192/ℚ19 recovers all $35$ affine sporadic quadratic divisors on $X(s3,ns5)$ over ℚ(√5). Completeness is proved in an appendix using symmetric Chabauty and a Mordell--Weil sieve.
Related
- Lubin-Tate representations over nontrivial finite Galois extensions of ℚp are not Aut-intrinsically Hodge-Tate
- MDS codes containing a fixed subcode over finite field extensions
- On MRD constacyclic codes over inseparable field extensions
- Canonical extensions of ruled surfaces over elliptic curves
- Finite-index extensions of essentially free countable Borel equivalence relations
BibTeX
@misc{cai2026explicit,
title = {{Explicit Coleman integration over finite extensions of $\mathbbQ_p$}},
author = {Yulin Cai and Timo Keller},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33970},
eprint = {2610.33970},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33970},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Explicit Coleman integration over finite extensions of ℚ_p
AU - Yulin Cai
AU - Timo Keller
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.33970
UR - https://arxiv.org/abs/2610.33970
AB - Coleman integration is an important computational ingredient of the Chabauty--Coleman method and its extensions. We extend the Balakrishnan--Tuitman algorithm to general smooth projective curves with good reduction over arbitrary finite extensions of ℚ_p, allowing both ramification and nontrivial residue degree. Given a suitable plane model and integral bases, we provide explicit precision bounds and an accompanying Magma implementation. As an application, a single-prime computation at p=19 over the unramified quadratic extension ℚ_19^2/ℚ_19 recovers all $35$ affine sporadic quadratic divisors on $X(s3,ns5)$ over ℚ(√5). Completeness is proved in an appendix using symmetric Chabauty and a Mordell--Weil sieve.
ER -