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Homomorphisms of multiplicative groups of fields preserving algebraic dependence

  • Fedor A. Bogomolov
  • Marat Rovinsky
  • Yuri Tschinkel
Research Article
  • 3 Downloads

Abstract

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

Keywords

Anabelian geometry Valuations Section conjecture 

Mathematics Subject Classification

14G32 11R32 11R58 14E08 19D45 

Notes

Acknowledgements

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
  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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