A consequence of the relative Bogomolov conjecture

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Vesselin Dimitrov
  • Ziyang Gao
  • Philipp Habegger

Research Organisations

External Research Organisations

  • University of Cambridge
  • University of Basel
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Details

Original languageEnglish
Pages (from-to)146-160
Number of pages15
JournalJournal of Number Theory
Volume230
Early online date19 Oct 2021
Publication statusPublished - Jan 2022

Abstract

We propose a formulation of the relative Bogomolov conjecture and show that it gives an affirmative answer to a question of Mazur's concerning the uniformity of the Mordell-Lang conjecture for curves. In particular we show that the relative Bogomolov conjecture implies the uniform Manin-Mumford conjecture for curves. The proof is built up on our previous work "Uniformity in Mordell-Lang for curves".

Keywords

    math.NT, math.AG, 11G30, 11G50, 14G05, 14G25, Uniform Mordell-Lang, Relative Bogomolov conjecture, Height theory, Families of Abelian varieties

ASJC Scopus subject areas

Cite this

A consequence of the relative Bogomolov conjecture. / Dimitrov, Vesselin; Gao, Ziyang; Habegger, Philipp.
In: Journal of Number Theory, Vol. 230, 01.2022, p. 146-160.

Research output: Contribution to journal › Article › Research › peer review

Dimitrov V, Gao Z, Habegger P. A consequence of the relative Bogomolov conjecture. Journal of Number Theory. 2022 Jan;230:146-160. Epub 2021 Oct 19. doi: 10.1016/j.jnt.2021.03.028
Dimitrov, Vesselin ; Gao, Ziyang ; Habegger, Philipp. / A consequence of the relative Bogomolov conjecture. In: Journal of Number Theory. 2022 ; Vol. 230. pp. 146-160.
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note = "Funding Information: Acknowledgments. We would like to thank the referee for their comments. Vesselin Dimitrov has received funding from the European Union's Seventh Framework Programme (FP7/2007?2013) / ERC grant agreement n? 617129. Ziyang Gao has received fundings from the French National Research Agency grant ANR-19-ERC7-0004, and the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement n? 945714). Philipp Habegger has received funding from the Swiss National Science Foundation (grant n? 200020_184623).",
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