Skip to main content
SpringerLink
Log in

Nilpotent connections and the monodromy theorem: Applications of a result of turrittin

  • Published:
Publications Mathématiques de l'Institut des Hautes Études Scientifiques Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. M. Atiyah andW. Hodge, Integrals of the second kind on an algebraic variety,Annals of Math.,62 (1955). 56–91.

    Article  MathSciNet  Google Scholar 

  2. P. Berthelot, Cohomologiep-cristalline des schémas, I, II, III,C. R. Acad. Sc., Paris,269, sér. A (1969), 297–300, 357–360, and 397–400.

    MATH  MathSciNet  Google Scholar 

  3. E. Brieskorn,Die monodromie der isolierten Singularitäten von Hyperflächen (to appear).

  4. P. Cartier, Une nouvelle opération sur les formes différentielles,C. R. Acad. Sc. Paris,244 (1957), 426–428.

    MATH  MathSciNet  Google Scholar 

  5. ———,, Questions de rationalité des diviseurs en géométrie algébrique,Bull. Soc. Math. France,86 (1958), 177–251.

    MATH  MathSciNet  Google Scholar 

  6. H. Clemens, Picard-Lefschetz theorem for families of nonsingular algebraic varieties acquiring ordinary singularities,Trans. Amer. Math. Soc.,136 (1969), 93–108.

    Article  MATH  MathSciNet  Google Scholar 

  7. P. Deligne, Théorème de Lefschetz et critères de dégénérescence de suites spectrales,Publ. Math. I.H.E.S.,35 (1969).

  8. ---,Théorie de Hodge (to appear).

  9. L. Fuchs, Zur theorie der linearen Differentialgleichungen mit veränderlichen Coefficienten,J. für reine u. angew. Math.,66 (1866), 121–160, and68 (1868), 354–385.

    Article  MATH  Google Scholar 

  10. P. Griffiths, Periods of integrals on algebraic manifolds, I, II,Amer. J. Math.,90 (1968), 568–626 and 805–865.

    Article  MATH  MathSciNet  Google Scholar 

  11. ---,Monodromy of Homology and Periods of Integrals on Algebraic Manifolds, Lecture Notes, Princeton University, 1968.

  12. ---, Report on variation of Hodge structure, to appear inBull. Amer. Math. Soc.

  13. ———,, Periods of certain rational integrals, I, II,Ann. of Math.,90 (1969), 460–541.

    Article  Google Scholar 

  14. A. Grothendiecket al., SGA,7 (to appear).

  15. -- andJ. Dieudonné, Eléments de géométrie algébrique, chap. 3, Part. 2,Publ. Math. I.H.E.S.,17 (1963).

  16. ---,Fondements de la géométrie algébrique, Secrétariat mathématique, II, rue Pierre-Curie, Paris (5e), 1962.

  17. ---, On the de Rham Cohomology of Algebraic Varieties,Publ. Math. I.H.E.S.,29 (1966).

  18. ———,,et al., Crystals and de Rham cohomology, inDix exposés sur la cohomologie des schémas, Amsterdam, North-Holland, 1969.

    Google Scholar 

  19. H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic, zero, I, II,Ann. of Math.,79 (1964), 109–326.

    Article  MathSciNet  Google Scholar 

  20. G. Hochschild, B. Kostant andA. Rosenberg, Differential forms on regular affine algebras,Trans. Amer. Math. Soc.,102 (1962), 383–408.

    Article  MATH  MathSciNet  Google Scholar 

  21. E. Ince,Ordinary Differential Equations, New York, Dover, 1956.

    Google Scholar 

  22. N. Katz, On the Differential Equations Satisfied by Period Matrices,Publ. Math. I.H.E.S.,35 (1968).

  23. K. Kodaira andD. C. Spencer, On deformations of complex structures, I, II,Ann. of Math.,67 (1958), 328–466.

    Article  MathSciNet  Google Scholar 

  24. A. Landman,On the Picard-Lefschetz Formula for Algebraic Manifolds Acquiring General Singularities, Berkeley Ph. D. thesis, 1966.

  25. D. Lutz, Some characterizations of systems of linear differential equations having regular singular solutions,Trans. Amer. Math. Soc.,126 (1967), 427–441.

    Article  MATH  MathSciNet  Google Scholar 

  26. Ju. Manin, Moduli Fuchsiani,Annali Scuola Norm. Sup. Pisa, sér. III,19 (1965), 113–126.

    MATH  MathSciNet  Google Scholar 

  27. ---, Algebraic curves over fields with differentiation,AMS Translations, (2),37, 59–78.

  28. ---, Rational points of algebraic curves over function fields,AMS Translations, (2),50, 189–234.

  29. ---, The Hasse-Witt matrix of an algebraic curve,AMS Translations, (2),45, 245–264.

  30. D. Mumford, Lectures on Curves on an Algebraic Surface,Ann. of Math. Studies, Princeton,59 (1966).

  31. T. Oda, The First de Rham Cohomology Group and Dieudonné Modules,Annales scientifiques de l’Ecole Norm. Sup., 4e série, t. 2, 1969.

  32. ———,, andN. Katz, On the differentiation of de Rham cohomology classes with respect to parameters,J. Math. Kyoto Univ.,8 (1968), 199–213.

    MATH  MathSciNet  Google Scholar 

  33. E. Picard andG. Simart,Théorie des fonctions algébriques de deux variables indépendantes, I, chap. IV, Paris, Gauthier-Villars, 1897.

    MATH  Google Scholar 

  34. J.-P. Serre andJ. Tate, Good reduction of abelian varieties,Ann. of Math.,88 (1968), 492–517.

    Article  MathSciNet  Google Scholar 

  35. H. L. Turrittin, Convergent solutions of ordinary homogeneous differential equations in the neighborhood of an irregular singular point,Acta Math.,93 (1955), 27–66.

    Article  MATH  MathSciNet  Google Scholar 

  36. ---, Asymptotic expansions of solutions of systems of ordinary linear differential equations containing a parameter,in S. Lefschetz (ed.), Contributions to the Theory of Nonlinear Oscillations,Annals of Math. Studies, Princeton,29 (1952).

Download references

Authors
  1. Nicholas M. Katz
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Katz, N.M. Nilpotent connections and the monodromy theorem: Applications of a result of turrittin. Publications Mathématiques de L’Institut des Hautes Scientifiques 39, 175–232 (1970). https://doi.org/10.1007/BF02684688

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02684688

Keywords

Search

Navigation