A uniform quantitative Manin–Mumford theorem for curves over function fields
-
Nicole Looper
,
Joseph Silverman
Abstract
We prove that any smooth projective geometrically connected non-isotrivial curve of genus
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1803021
Funding source: Simons Foundation
Award Identifier / Grant number: 712332
Award Identifier / Grant number: 200020_184623
Funding statement: The first author was supported by NSF grant DMS-1803021. The second author was partially supported by Simons Collaboration Grant #712332. The third author was supported by the Swiss National Science Foundation grant “Diophantine Equations: Special Points, Integrality, and Beyond” (nº 200020_184623).
Acknowledgements
The authors would like to thank Matt Baker, Alex Carney, Robin de Jong, Xander Faber, Myrto Mavraki, and Lucia Mocz for their helpful conversations and useful insights on the admissible pairing. We also thank Jiawei Yu for pointing out an improvement in the bound for 𝜖 in Theorem 1.3, as well as the editor for the suggestion of adding Corollary 1.2. We thank the anonymous referees for their very careful reading and useful comments on two drafts of this paper.
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