Nilpotent connections and the monodromy theorem : applications of a result of Turrittin
Publications Mathématiques de l'IHÉS (1970)
- Volume: 39, page 175-232
- ISSN: 0073-8301
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topKatz, Nicholas M.. "Nilpotent connections and the monodromy theorem : applications of a result of Turrittin." Publications Mathématiques de l'IHÉS 39 (1970): 175-232. <http://eudml.org/doc/103909>.
@article{Katz1970,
author = {Katz, Nicholas M.},
journal = {Publications Mathématiques de l'IHÉS},
language = {eng},
pages = {175-232},
publisher = {Institut des Hautes Études Scientifiques},
title = {Nilpotent connections and the monodromy theorem : applications of a result of Turrittin},
url = {http://eudml.org/doc/103909},
volume = {39},
year = {1970},
}
TY - JOUR
AU - Katz, Nicholas M.
TI - Nilpotent connections and the monodromy theorem : applications of a result of Turrittin
JO - Publications Mathématiques de l'IHÉS
PY - 1970
PB - Institut des Hautes Études Scientifiques
VL - 39
SP - 175
EP - 232
LA - eng
UR - http://eudml.org/doc/103909
ER -
References
top- [0] M. ATIYAH and W. HODGE, Integrals of the second kind on an algebraic variety, Annals of Math., 62 (1955), 56-91. Zbl0068.34401MR17,533d
- [1] P. BERTHELOT, Cohomologie p-cristalline des schémas, I, II, III, C. R. Acad. Sc., Paris, 269, sér. A (1969), 297-300, 357-360, and 397-400. Zbl0179.26301MR40 #151
- [2] E. BRIESKORN, Die monodromie der isolierten Singularitäten von Hyperflächen (to appear). Zbl0186.26101
- [3] P. CARTIER, Une nouvelle opération sur les formes différentielles, C. R. Acad. Sc. Paris, 244 (1957), 426-428. Zbl0077.04502MR18,870b
- [4] P. CARTIER, Questions de rationalité des diviseurs en géométrie algébrique, Bull. Soc. Math. France, 86 (1958), 177-251. Zbl0091.33501MR21 #4957
- [5] H. CLEMENS, Picard-Lefschetz theorem for families of nonsingular algebraic varieties acquiring ordinary singularities, Trans. Amer. Math. Soc., 136 (1969), 93-108. Zbl0185.51302MR38 #2135
- [6] P. DELIGNE, Théorème de Lefschetz et critères de dégénérescence de suites spectrales, Publ. Math. I.H.E.S., 35 (1969). Zbl0159.22501
- [7] P. DELIGNE, Théorie de Hodge (to appear). Zbl0219.14006
- [8] L. FUCHS, Zur theorie der linearen Differentialgleichungen mit veränderlichen Coefficienten, J. für reine u. angew. Math., 66 (1866), 121-160, and 68 (1868), 354-385.
- [9] P. GRIFFITHS, Periods of integrals on algebraic manifolds, I, II, Amer. J. Math., 90 (1968), 568-626 and 805-865. Zbl0169.52303MR37 #5215
- [10] P. GRIFFITHS, Monodromy of Homology and Periods of Integrals on Algebraic Manifolds, Lecture Notes, Princeton University, 1968. MR39 #4171
- [11] P. GRIFFITHS, Report on variation of Hodge structure, to appear in Bull. Amer. Math. Soc.
- [12] P. GRIFFITHS, Periods of certain rational integrals, I, II, Ann. of Math., 90 (1969), 460-541. Zbl0215.08103MR41 #5357
- [13] A. GROTHENDIECK et al., SGA, 7 (to appear). Zbl1079.14001
- [14] A. GROTHENDIECK and J. DIEUDONNÉ, Eléments de géométrie algébrique, chap. 3, Part. 2, Publ. Math. I.H.E.S., 17 (1963). Zbl0122.16102
- [15] A. GROTHENDIECK, Fondements de la géométrie algébrique, Secrétariat mathématique, 11, rue Pierre-Curie, Paris (5e), 1962. Zbl0239.14002
- [16] A. GROTHENDIECK, On the de Rham Cohomology of Algebraic Varieties, Publ. Math. I.H.E.S., 29 (1966). Zbl0145.17602MR33 #7343
- [17] A. GROTHENDIECK, Crystals and de Rham cohomology, in Dix exposés sur la cohomologie des schémas, Amsterdam, North-Holland, 1969. Zbl0215.37102
- [18] H. HIRONAKA, Resolution of singularities of an algebraic variety over a field of characteristic, zero, I, II, Ann. of Math., 79 (1964), 109-326. Zbl0122.38603MR33 #7333
- [19] G. HOCHSCHILD, B. KOSTANT and A. ROSENBERG, Differential forms on regular affine algebras, Trans. Amer. Math. Soc., 102 (1962), 383-408. Zbl0102.27701MR26 #167
- [20] E. INCE, Ordinary Differential Equations, New York, Dover, 1956. Zbl0063.02971
- [21] N. KATZ, On the Differential Equations Satisfied by Period Matrices, Publ. Math. I.H.E.S., 35 (1968). Zbl0159.22502MR39 #4168
- [22] K. KODAIRA and D. C. SPENCER, On deformations of complex structures, I, II, Ann. of Math., 67 (1958), 328-466. Zbl0128.16901MR22 #3009
- [23] A. LANDMAN, On the Picard-Lefschetz Formula for Algebraic Manifolds Acquiring General Singularities, Berkeley Ph. D. thesis, 1966. Zbl0284.14005
- [24] D. LUTZ, Some characterizations of systems of linear differential equations having regular singular solutions, Trans. Amer. Math. Soc., 126 (1967), 427-441. Zbl0153.11102MR34 #6189
- [25] Ju. MANIN, Moduli Fuchsiani, Annali Scuola Norm. Sup. Pisa, sér. III, 19 (1965), 113-126. Zbl0166.04301MR31 #4815
- [26] Ju. MANIN, Algebraic curves over fields with differentiation, AMS Translations, (2), 37, 59-78. Zbl0151.27601
- [27] Ju. MANIN, Rational points of algebraic curves over function fields, AMS Translations, (2), 50, 189-234. Zbl0178.55102
- [28] Ju. MANIN, The Hasse-Witt matrix of an algebraic curve, AMS Translations, (2), 45, 245-264. Zbl0148.28002
- [29] D. MUMFORD, Lectures on Curves on an Algebraic Surface, Ann. of Math. Studies, Princeton, 59 (1966). Zbl0187.42701MR35 #187
- [30] T. ODA, The First de Rham Cohomology Group and Dieudonné Modules, Annales scientifiques de l'Ecole Norm. Sup., 4e série, t. 2, 1969. Zbl0175.47901MR39 #2775
- [31] T. ODA and N. KATZ, On the differentiation of de Rham cohomology classes with respect to parameters, J. Math. Kyoto Univ., 8 (1968), 199-213. Zbl0165.54802MR38 #5792
- [32] E. PICARD and G. SIMART, Théorie des fonctions algébriques de deux variables indépendantes, I, chap. IV, Paris, Gauthier-Villars, 1897. Zbl37.0404.02JFM28.0327.01
- [33] J.-P. SERRE and J. TATE, Good reduction of abelian varieties, Ann. of Math., 88 (1968), 492-517. Zbl0172.46101MR38 #4488
- [34] H. L. TURRITTIN, Convergent solutions of ordinary homogeneous differential equations in the neighborhood of an irregular singular point, Acta Math., 93 (1955), 27-66. Zbl0064.33603MR16,925a
- [35] H. L. TURRITTIN, 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, Pricenton, 29 (1952). Zbl0047.08602MR14,377a
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- Arthur Ogus, Cohomology of the infinitesimal site
- B. Malgrange, Sur les points singuliers des équations différentielles (fin)
- Fabrizio Andreatta, Adrian Iovita, Semistable Sheaves and Comparison Isomorphisms in the Semistable Case
- Nicholas M. Katz, A conjecture in the arithmetic theory of differential equations
- Yves Andre, Équations différentielles -adiques et dégénérescence de groupes de Hodge
- Philippe Robba, Lemmes de Hensel pour les opérateurs différentiels, II
- Takuro Mochizuki, On Deligne-Malgrange lattices, resolution of turning points and harmonic bundles
- Hô Hai Phùng, Gauss-Manin stratification and stratified fundamental group schemes
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