European Journal of Mathematics

, Volume 5, Issue 3, pp 656–685 | Cite as

Homomorphisms of multiplicative groups of fields preserving algebraic dependence

  • Fedor A. Bogomolov
  • Marat Rovinsky
  • Yuri TschinkelEmail author
Research Article


We study homomorphisms of multiplicative groups of fields preserving algebraic dependence and show that such homomorphisms give rise to valuations.


Anabelian geometry Valuations Section conjecture 

Mathematics Subject Classification

14G32 11R32 11R58 14E08 19D45 



We are very grateful to the referees for their careful reading of the first version of the paper, which helped us to improve the exposition.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Fedor A. Bogomolov
    • 1
    • 2
  • Marat Rovinsky
    • 2
  • Yuri Tschinkel
    • 1
    • 3
    Email author
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.AG LaboratoryNational Research University Higher School of EconomicsMoscowRussia
  3. 3.Simons FoundationNew YorkUSA

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