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Mathematics > Number Theory

arXiv:2201.11077 (math)
[Submitted on 26 Jan 2022 (v1), last revised 28 Oct 2022 (this version, v2)]

Title:Bounds on the number of rational points of curves in families

Authors:Pedro Lemos, Alex Torzewski
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Abstract:In this note, we give an alternative proof of uniform boundedness of the number of integral points of smooth projective curves over a fixed number field with good reduction outside of a fixed set of primes. We use that due to Bertin-Romagny, the Kodaira-Parshin families constructed by Lawrence-Venkatesh can themselves be assembled into a family. We then repeat Lawrence-Venkatesh's study of the p-adic period map, together with the comparison of nearby fibres.
Comments: 12 pages, version to appear in the Bulletin of the London Mathematical Society
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
MSC classes: 11D45, 14G05 (primary) 11D88, 14H30, 14H40 (secondary)
Cite as: arXiv:2201.11077 [math.NT]
  (or arXiv:2201.11077v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.2201.11077

Submission history

From: Alex Torzewski [view email]
[v1] Wed, 26 Jan 2022 17:34:04 UTC (37 KB)
[v2] Fri, 28 Oct 2022 09:17:58 UTC (41 KB)
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