×

zbMATH — the first resource for mathematics

Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin. (English) Zbl 0221.14007

MSC:
14F40 de Rham cohomology and algebraic geometry
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
53C05 Connections (general theory)
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML
References:
[1] M. Atiyah andW. Hodge, Integrals of the second kind on an algebraic variety,Annals of Math.,62 (1955). 56–91. · Zbl 0068.34401
[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.
[3] E. Brieskorn,Die monodromie der isolierten Singularitäten von Hyperflächen (to appear). · Zbl 0214.20101
[4] P. Cartier, Une nouvelle opération sur les formes différentielles,C. R. Acad. Sc. Paris,244 (1957), 426–428. · Zbl 0077.04502
[5] ——,, Questions de rationalité des diviseurs en géométrie algébrique,Bull. Soc. Math. France,86 (1958), 177–251.
[6] H. Clemens, Picard-Lefschetz theorem for families of nonsingular algebraic varieties acquiring ordinary singularities,Trans. Amer. Math. Soc.,136 (1969), 93–108. · Zbl 0185.51302
[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. · ERAM 066.1719cj
[10] P. Griffiths, Periods of integrals on algebraic manifolds, I, II,Amer. J. Math.,90 (1968), 568–626 and 805–865. · Zbl 0169.52303
[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. · Zbl 0215.08103
[14] A. Grothendieck et al., SGA,7 (to appear). · Zbl 1079.14001
[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). · Zbl 0145.17602
[18] ——,,et al., Crystals and de Rham cohomology, inDix exposés sur la cohomologie des schémas, Amsterdam, North-Holland, 1969.
[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. · Zbl 0122.38603
[20] G. Hochschild, B. Kostant andA. Rosenberg, Differential forms on regular affine algebras,Trans. Amer. Math. Soc.,102 (1962), 383–408. · Zbl 0102.27701
[21] E. Ince,Ordinary Differential Equations, New York, Dover, 1956. · Zbl 0063.02971
[22] N. Katz, On the Differential Equations Satisfied by Period Matrices,Publ. Math. I.H.E.S.,35 (1968). · Zbl 0159.22502
[23] K. Kodaira andD. C. Spencer, On deformations of complex structures, I, II,Ann. of Math.,67 (1958), 328–466. · Zbl 0128.16901
[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. · Zbl 0153.11102
[26] Ju. Manin, Moduli Fuchsiani,Annali Scuola Norm. Sup. Pisa, sér. III,19 (1965), 113–126.
[27] —, Algebraic curves over fields with differentiation,AMS Translations, (2),37, 59–78. · Zbl 0151.27601
[28] —, Rational points of algebraic curves over function fields,AMS Translations, (2),50, 189–234. · Zbl 0178.55102
[29] —, The Hasse-Witt matrix of an algebraic curve,AMS Translations, (2),45, 245–264. · Zbl 0148.28002
[30] D. Mumford, Lectures on Curves on an Algebraic Surface,Ann. of Math. Studies, Princeton,59 (1966). · Zbl 0187.42701
[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. · Zbl 0165.54802
[33] E. Picard andG. Simart,Théorie des fonctions algébriques de deux variables indépendantes, I, chap. IV, Paris, Gauthier-Villars, 1897.
[34] J.-P. Serre andJ. Tate, Good reduction of abelian varieties,Ann. of Math.,88 (1968), 492–517. · Zbl 0172.46101
[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. · Zbl 0064.33603
[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). · Zbl 0047.08602
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.