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Surfaces of type K3 over fields of finite characteristic. (English. Russian original) Zbl 0518.14015

J. Sov. Math. 22, 1476-1533 (1983); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 18, 115-207 (1981).

MSC:

14G15 Finite ground fields in algebraic geometry
14J25 Special surfaces
14J15 Moduli, classification: analytic theory; relations with modular forms
14D10 Arithmetic ground fields (finite, local, global) and families or fibrations
14J10 Families, moduli, classification: algebraic theory
14F30 \(p\)-adic cohomology, crystalline cohomology
Full Text: DOI

References:

[1] Algebraic Surfaces, Tr. Mat. Inst. im. V. A. Steklova,75 (1965).
[2] B. B. Venkov, ?On the classification of integral, even, unimodular, 24-dimensional quadratic forms,? Tr. Mat. Inst. im. V. S. Steklova,148, 65?76 (1978). · Zbl 0443.10021
[3] I. V. Dolgachev, ?The Euler characteristic of algebraic varieties,? Mat. Sb.,89, No. 2, 297?312 (1972). · Zbl 0226.14003
[4] V. S. Kulikov, ?Degenerations of K3 surfaces,? Izv. Akad. Nauk SSSR, Ser. Mat.,41, No. 5, 1008?1042 (1977).
[5] V. V. Nikulin, ?Integral symmetric bilinear forms and some of their geometric applications,? Izv. Akad. Nauk SSSR, Ser. Mat.,43, No. 1, 111?177 (1979). · Zbl 0408.10011
[6] I. I. Pyatetskii-Shapiro and I. R. Shafarevich, ?The Torelli theorem for algebraic surfaces of type K3,? Izv. Akad. Nauk SSSR, Ser. Mat.,35, 530?572 (1971).
[7] A. N. Rudakov and I. R. Shafarevich, ?Nonseparable morphisms of algebraic surfaces,? Izv. Akad. Nauk SSSR, Ser. Mat.,40, No. 6, 1269?1307 (1976).
[8] A. N. Rudakov and I. R. Shafarevich, ?Supersingular surfaces of type K3 over fields of characteristic 2,? Izv. Akad. Nauk SSSR, Ser. Mat.,42, No. 4, 848?869 (1978). · Zbl 0424.14008
[9] A. N. Rudakov and I. R. Shafarevich, ?Vector fields on elliptic surfaces,? Usp. Mat. Nauk,33, No. 6, 231?232 (1978). · Zbl 0411.14008
[10] M. Artin, ?Supersingular K3 surfaces,? Ann. Sc. Ec. Norm. Sup. 4-e Serie,7, fase 4, 543?567 (1974).
[11] M. Artin, ?Algebraic construction of Breskorn’s resolution,? J. Algebra,29, 330?348 (1974). · Zbl 0292.14013 · doi:10.1016/0021-8693(74)90102-1
[12] M. Artin and B. Mazur, ?Formal groups arising from algebraic varieties,? Ann. Sc. Ec. Norm. Sup. 4-e serie,10, 87?132 (1977).
[13] P. Berthelot, ?Cohomologie cristalline des schemas de characteristique p > 0,? Lect. Notes Math.,407 (1974). · Zbl 0298.14012
[14] P. Berthelot and A. Ogus, Notes on Crystalline Cohomology, Princeton Univ. Press (1978). · Zbl 0383.14010
[15] E. Bombieri and D. Husemoller, ?The classification and embeddings of surfaces,? Proc. of Symposia in Pure Mathematics,29, 329?421 (1974). · Zbl 0326.14009 · doi:10.1090/pspum/029/0506292
[16] E. Bombieri and D. Mumford, ?Enriques’ classification of surfaces in char. p. III,? Inventiones Mathem.,35, 197?232 (1976). · Zbl 0336.14010 · doi:10.1007/BF01390138
[17] N. Bourbaki, Groupes et Algébras de Lie, Chaps. 4, 5, et 6, Eléments de Mathématique, Fasc. XXXIV, Paris (1968).
[18] C. Chevalley, Introduction to the Theory of Algebraic Functions of One Variable, Baltimore (1951). · Zbl 0045.32301
[19] P. Deligne, ?Relèvements des surfaces K3 en characteristique nulle (rédigé par L. Illusie),? Preprint (1979).
[20] P. Deligne (avec la collaboration de L. Illusie), ?Cristaux ordinaires et coordonnées canoniques,? Preprint (1979). · Zbl 0537.14012
[21] D. Giescker, ?Global moduli for surfaces of general type,? Preprint (1979).
[22] A. Grothendieck, ?Eléments de géométrie algébrique. III,? Publications Mathématiques, No. 11, 349?511 (1961).
[23] A. Grothendieck, ?Le groupe de Brauer. III,? Dix Exposés sur la Cohomologie des Schémas, Paris-Amsterdam (1968), pp. 88?188.
[24] L. Illusie, ?Report on crystalline cohomology,? Proceedings of Symposia in Pure Mathematics,29, 459?479 (1974). · doi:10.1090/pspum/029/0393034
[25] N. Jacobson, Lie Algebras, New York-London (1962). · Zbl 0121.27504
[26] N. Katz, ?Algebraic solutions of differential equations, p-curvature and the Hodge filtration,? Inventiones Mathem.,18, 1?118 (1972). · Zbl 0278.14004 · doi:10.1007/BF01389714
[27] N. Katz, ?Travaux de Dwork,? Séminaire Bourbaki, exp. 409, Lecture Notes in Math.,317 (1973), pp. 167?200. · doi:10.1007/BFb0069282
[28] S. Lang, Elliptic Functions, Addison-Wesley, Reading, Mass. (1974).
[29] D. Mumford, Geometric Invariant Theory, Springer-Verlag, Berlin (1965). · Zbl 0147.39304
[30] M. Nagata, Local Rings, Wiley-Interscience, New York (1962).
[31] A. Ogg, ?Elliptic curves and wild ramification,? Am. J. Math.,89, No. 1, 1?21 (1967). · Zbl 0147.39803 · doi:10.2307/2373092
[32] A. Ogus, ?F-crystals and Griffiths transversality,? Int. Symp. on Alg. Geometry, Kyoto (1977), pp. 15?44.
[33] A. Ogus, ?Supersingular K3-crystals,? Astérisque,64, 3?86 (1979). · Zbl 0435.14003
[34] T. O’Meara, The Arithmetic Theory of Quadratic Forms, New York (1950).
[35] P. Russel, ?Forms of the affine line and its additive group,? Pac. J. Math.,79, No. 3, 411?449 (1964).
[36] M. Schlessinger, ?Functors of Artin rings,? Trans. Am. Math. Soc.,130, 205?222 (1968). · Zbl 0167.49503 · doi:10.1090/S0002-9947-1968-0217093-3
[37] J. P. Serre, Cours d’Arithmétique, Presses Univ. de France, Paris (1970).
[38] C. S. Seshadri, L’Operation de Cartier. Applications. Variétés de Picard, Seminaire C. Chevalley, Paris (1960).
[39] T. Shioda, ?An example of unirational surfaces in characteristic p,? Math. Ann.,211, 233?236 (1974). · Zbl 0276.14018 · doi:10.1007/BF01350715
[40] T. Shioda, ?Algebraic cycles on certain K3 surfaces in characteristic p,? Proceedings of the International Conference on Manifolds and Related Topics in Topology, Univ. of Tokyo Press (1975), pp. 357?364. · Zbl 0311.14007
[41] T. Shioda, ?Some results on unirationality of algebraic surfaces,? Math. Ann.,230, 153?168 (1977). · Zbl 0343.14021 · doi:10.1007/BF01370660
[42] T. Shioda, ?Kummer surfaces in characteristic 2,? Proc. Jpn. Acad.,50, No. 9, 718?722 (1974). · Zbl 0332.14015 · doi:10.3792/pja/1195518796
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