Newton polygons and p-divisible groups: a conjecture by Grothendieck
Formes automorphes (I) - Actes du semestre du centre Émile Borel, printemps 2000, Astérisque, no. 298 (2005), pp. 255-269.
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     booktitle = {Formes automorphes (I) - Actes du semestre du centre \'Emile Borel, printemps 2000},
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Oort, Frans. Newton polygons and $p$-divisible groups: a conjecture by Grothendieck, dans Formes automorphes (I) - Actes du semestre du centre Émile Borel, printemps 2000, Astérisque, no. 298 (2005), pp. 255-269. http://archive.numdam.org/item/AST_2005__298__255_0/

[1] C.-L. Chai - Every ordinary symplectic isogeny class in positive characteristic is dense in the moduli, Invent. Math. 121 (1995), p. 439-479. | DOI | EuDML | MR | Zbl

[2] C.-L. Chai & F. Oort - Hecke orbits, in preparation.

[3] G. Van Der Geer - Cycles on the moduli space of abelian varieties, in Moduli of curves and abelian varieties (The Dutch intercity seminar on moduli) (C. Faber & E. Looijenga, eds.), Aspects of Mathematics, vol. E 33, Vieweg, 1999, p. 65-89, see arXiv: alg--geom/9605011. | DOI | MR | Zbl

[4] A. Grothendieck - Groupes de Barsotti-Tate et cristaux de Dieudonné, Sém. Math. Sup. Univ. Montréal, Presses Univ. Montréal, 1974. | MR | Zbl

[5] A. Grothendieck & J. Dieudonné - Eléments de géométrie algébrique. Ch. III1: Étude cohomologique des faisceaux cohérents, vol. 11, Publ. Math. Inst. Hautes Etudes Sci., 1961. | Numdam | MR | Zbl

[6] A. J. De Jong - Crystalline Dieudonné module theory via formal rigid geometry, Publ. Math. Inst. Hautes Études Sci. 82 (1995), p. 5-96. | DOI | EuDML | Numdam | MR | Zbl

[7] A. J. De Jong, Homomorphisms of Barsotti-Tate groups and crystals in positive characteristic, Invent. Math. 134 (1998), p. 301-333. | DOI | MR | Zbl

[8] A. J. De Jong & F. Oort - Purity of the stratification by Newton polygons, J. Amer. Math. Soc. 13 (2000), p. 209-241, see: http://www.ams.org/jams. | DOI | MR | Zbl

[9] A. J. De Jong & F. Oort, Purity of the stratification by Newton polygons, J. Amer. Math. Soc. 13 (2000), p. 209-241. | DOI | MR | Zbl

[10] T. Katsura & F. Oort - Supersingular abelian varieties of dimension two or three and class numbers, in Algebraic geometry (Sendai, 1985) (T. Oda, éd.), Advanced Studies in Pure Math., vol. 10, Kinokuniya Cy Tokyo and North-Holland Cy Amsterdam, 1987, p. 253-281. | DOI | MR | Zbl

[11] N. M. Katz - Slope nitrations of F-crystals, in Journées de Géométrie Algébrique (Rennes), Vol. I, Astérisque, vol. 63, Société Mathématique de France, 1979. | Numdam | MR

[12] N. M. Katz, Serre-Tate local moduli, in Surfaces algébriques (Sém. de géométrie algébrique d'Orsay 1976-78), Lect. Notes in Math., vol. 868, Springer-Verlag, 1981, Exp. n° V-bis, p. 138-202. | MR | Zbl

[13] S. Keel & L. Sadun - Oort's conjecture for A g , J. Amer. Math. Soc. 16 (2003), p. 887-900. | DOI | MR | Zbl

[14] K.-Z. Li & F. Oort - Moduli of supersingular abelian varieties, Lect. Notes in Math., vol. 1680, Springer-Verlag, 1998. | MR | Zbl

[15] Yu. I. Manin - The theory of commutative formal groups over fields of finite characteristic, Uspekhi Mat. Nauk 18 (1963), p. 3-90, Engl, transl: Russ. Math. Surveys 18 (1963), p. 1-80. | MR | Zbl

[16] D. Mumford - Geometric invariant theory, Ergebnisse Math., Neue Folge, vol. 34, Springer-Verlag, 1965. | MR | Zbl

[17] P. Norman - An algorithm for computing local moduli of abelian varieties, Ann. of Math. 101 (1975), p. 499-509. | DOI | MR | Zbl

[18] P. Norman & F. Oort - Moduli of abelian varieties, Ann. of Math. 112 (1980), p. 413-439. | DOI | MR | Zbl

[19] T. Oda & F. Oort - Supersingular abelian varieties, in Proceedings International Symp. on Algebraic Geometry (Kyoto, 1977) (M. Nagata, ed.), Kinokuniya, 1978, p. 595-621. | MR | Zbl

[20] F. Oort - Moduli of abelian varieties and Newton polygons, C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), p. 385-389. | MR | Zbl

[21] F. Oort, Newton polygons and formal groups: conjectures by Manin and Grothendieck, Ann. of Math. 152 (2000), p. 183-206. | DOI | EuDML | MR | Zbl

[22] F. Oort, Newton polygons and formal groups: conjectures by Manin and Grothendieck, Ann. of Math. 152 (2000), p. 183-206. | DOI | EuDML | MR | Zbl

[23] F. Oort, Newton polygon strata in the moduli space of abelian varieties, in Moduli of abelian varieties (C. Faber, G. van der Geer & F. Oort, eds.), Progress in Math., vol. 195, Birkhäuser Verlag, 2001, p. 417-440. | DOI | MR | Zbl

[24] F. Oort, Newton polygon strata in the moduli space of abelian varieties, in Moduli of abelian varieties (C. Faber, G. van der Geer & F. Oort, eds.), Progress in Math., vol. 195, Birkhäuser Verlag, 2001, p. 417-440. | DOI | MR | Zbl

[25] F. Oort, Foliations in moduli spaces of abelian varieties, J. Amer. Math. Soc. 17 (2004), p. 267-296. | DOI | MR | Zbl

[26] F. Oort, Simple finite group schemes, to appear. | Numdam | MR

[27] F. Oort, Minimal p-divisible groups, to appear in Ann. of Math. | MR | Zbl

[28] J. Tate - Classes d'isogénie de variétés abéliennes sur un corps fini (d'après T. Honda), in Sém. Bourbaki 1968/69, Lect. Notes in Math., vol. 179, Springer-Verlag, 1971, Exp. n° 352. | DOI | EuDML | Numdam | MR | Zbl

[29] T. Zink - A Dieudonné theory for p-divisible groups, in Class Field Theory, Its Centenary and Prospect, Advanced Studies in Pure Math., Kinokuniya, Tokyo, 2000, p. 1-22. | MR | Zbl

[30] T. Zink, The display of a formal p-divisible group, in Cohomologies p-adiques et applications arithmétiques, I (P. Berthelot, J.-M. Fontaine, L. Illusie, K. Kato & M. Rapoport, eds.), Astérisque, vol. 278, Société Mathématique de France, 2002. | Numdam | MR | Zbl