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Geometric properties of curves defined over number fields

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Abstract

The article contains a detailed proof of the famous Belyi theorem on geometry of complex algebraic curves defined over number fields. It also includes the discussion of several constructions and conjectures inspired by Belyi’s result which where brought up by the first author during his colloquium talks at different universities within the period from 1979 to 1984.

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Acknowledgements

The first author wants to thank Arman Sarikyan for his help in editing and preparation of the initial Max Planck Institute preprint for publication.

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012, USA

    Fedor A. Bogomolov

  2. Laboratory of Algebraic Geometry and its Applications, National Research University Higher School of Economics, 6 Usacheva Street, Moscow, Russia, 119048

    Fedor A. Bogomolov

  3. Haverford College, 370 Lancaster Avenue, Haverford, PA, 19041, USA

    Dale Husemöller

Authors
  1. Fedor A. Bogomolov
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  2. Dale Husemöller
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Correspondence to Fedor A. Bogomolov.

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The first author is partially supported by the HSE University Basic Research Program, Russian Academic Excellence Project ‘5-100’ and by EPSRC programme Grant EP/M024830.

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Bogomolov, F.A., Husemöller, D. Geometric properties of curves defined over number fields. European Journal of Mathematics 8, 792–805 (2022). https://doi.org/10.1007/s40879-021-00497-2

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