The generic fibre of finite group schemes; a “finite wild” criterion for good reduction of Abelian varieties
Izvestiya. Mathematics, Tome 70 (2006) no. 4, pp. 661-691 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the generic fibre functor for finite group schemes over the rings of integers of complete discrete valuation fields. We prove that it is “almost full”. Whence we deduce a “finite wild” criterion for good reduction of Abelian varieties.
Keywords: Group scheme, complete discrete valuation field, generic fibre.
Mots-clés : Cartier-Dieudonne module, formal group
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     title = {The generic fibre of finite group schemes; a {\textquotedblleft}finite wild{\textquotedblright} criterion for good reduction of {Abelian} varieties},
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M. V. Bondarko. The generic fibre of finite group schemes; a “finite wild” criterion for good reduction of Abelian varieties. Izvestiya. Mathematics, Tome 70 (2006) no. 4, pp. 661-691. http://geodesic.mathdoc.fr/item/IM2_2006_70_4_a1/

[1] Bondarko M. V., Vostokov S. V., “Yavnaya klassifikatsiya formalnykh grupp nad lokalnymi polyami”, Tr. MIAN, 241, 2003, 43–67 | MR | Zbl

[2] Bondarko M. V., “Yavnaya klassifikatsiya formalnykh grupp nad polnymi diskretno normirovannymi polyami s nesovershennym polem vychetov”, Tr. CPb. matem. ob-va, 11, 2005, 1–36

[3] Bondarko M. V., “Links between associated additive Galois modules and computation of $H^1$ for local formal group modules”, J. Number Theory, 101:1 (2003), 74–104 | DOI | MR | Zbl

[4] Conrad B., “Finite group schemes over bases with low ramification”, Compos. Math., 119:3 (1999), 239–326 | DOI | MR | Zbl

[5] Demazure M., Gabriel P., Groupes algébriques, Masson, Paris, 1970 | MR | Zbl

[6] Fontaine J.-M., Groupes $p$-divisibles sur les corps locaux, Astérisque, 47–48, 1977 | MR | Zbl

[7] Grothendieck A., “Modèles de Néron et monodromie”, Groupes de monodromie en géométrie algébrique. I, Séminaire de Géométrie Algébrique du Bois-Marie 1967–1969 (SGA 7 I), Expose IX, Lecture Notes in Math., 288, Springer-Verlag, Berlin–New York, 1972, 313–523 | MR | Zbl

[8] Hazewinkel M., Formal groups and applications, Pure Appl. Math., 78, Academic Press, New York–London, 1978 | MR | Zbl

[9] Milne J. S., Arithmetic duality theorems, Perspect. Math., 1, Academic Press, Boston, 1986 | MR | Zbl

[10] Oort F., “Dieudonné modules of finite local group schemes”, Indag. Math., 36 (1974), 284–292 | MR | Zbl

[11] Raynaud M., “Schemas en groupes de type $(p,\dots,p)$”, Bull. Soc. Math. France, 102 (1974), 241–280 | MR | Zbl