The Grothendieck Festschrift pp 199-227

Part of the Progress in Mathematics book series (MBC, volume 88)

Drawing Curves Over Number Fields

  • G. B. Shabat
  • V. A. Voevodsky

Abstract

This paper develops some of the ideas outlined by Alexander Grothendieck in his unpublished Esquisse d’un programme [0] in 1984.

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References

  1. [0]
    Grothendieck A., Esquisse d’un programme, Preprint 1984.Google Scholar
  2. [1]
    Belyi G.V., On Galots extensions of the maximal cyclotomic field (in Russian). Izvestiya An SSSR, ser. matem., 43:2 (1979), 269–276.Google Scholar
  3. [2]
    Mumford D., Curves and their Jacobians, Univ. of Michigan Press, 1975.MATHGoogle Scholar
  4. [3]
    Coxeter H.S.M. and Moser W.O.J., Generators and relations for discrete groups, Springer-Verlag, 1972.CrossRefMATHGoogle Scholar
  5. [4]
    Penner R.C., The Teichmuller Space of a Punctured Surface, preprint.Google Scholar
  6. [5]
    Klein F., Ueber die Transformation siebenter Ordnung der elliptischen Funktionen, Math. Ann. 14 B.3 (1878), 428–471.CrossRefMathSciNetGoogle Scholar
  7. [6]
    Hartshorne, R.S., Algebraic Geometry, Springer-Verlag, 1977.CrossRefMATHGoogle Scholar
  8. [7]
    Holzapfel, R.-P., Around Euler Partial Differential Equations, Berlin: Deutscher Verlag der Wissenschaften, 1986.Google Scholar
  9. [8]
    Yui, N., Explicit form of modular equations, J. Reine und Angew Math, 1978, Bd. 299–300.Google Scholar
  10. [9]
    Vladutz, S.G., Modular curves and the codes of polynomial complexity (in Russian). Preprint, 1978.Google Scholar
  11. [10]
    Voevodsky V.A., and Shabat G.B., Equilateral triangulations of Riemann surfaces and curves over algebraic number fields (in Russian). Doklady ANSSSR (1989), 204:2, 265–268.MathSciNetGoogle Scholar
  12. [11]
    Douady A. and Hubbard J., On the density of Strebel differentials. Invent. Math. (1975), 30 , N2, 175–179.CrossRefMATHMathSciNetGoogle Scholar
  13. [12]
    Boulatov D.V., Kazakov V.A., Kostov I.K., Migdal A.A., Analytical and numerical study of dynamically triangulated surfaces. Nucl. Phys. B275 [FS17] (1986), 641–686.CrossRefMATHMathSciNetGoogle Scholar
  14. [13]
    Manin Yu. I., Reflections on arithmetical physics, Talk at the Poiana-Brashov School on Strings and Conformai Field Theory, Sept. 1987, 1–14.Google Scholar
  15. [14]
    Itzyczon, C., Random Geometry, Lattices and Fields. “New perspectives in Quantum Field Theory”, Jaca (Spain), 1985.Google Scholar
  16. [15]
    Threlfall, W., Gruppenbilder, Abh. Sachs. Akad. Wiss. Math.-Phys. Kl.41, S. 1–59.Google Scholar
  17. [16]
    Abikoff, W., The Real-Analytic Theory of Teichmuller Space, Lecture Notes in Mathematics, Springer-Verlag, 820, 1980.Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • G. B. Shabat
    • 1
  • V. A. Voevodsky
    • 2
  1. 1.MoscowUSSR
  2. 2.Mech.-Math facultyMoscow State UniversityMoscowUSSR

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