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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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
@article{IM2_2006_70_4_a1,
     author = {M. V. Bondarko},
     title = {The generic fibre of finite group schemes; a ``finite wild'' criterion for good reduction of {Abelian} varieties},
     journal = {Izvestiya. Mathematics },
     pages = {661--691},
     publisher = {mathdoc},
     volume = {70},
     number = {4},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2006_70_4_a1/}
}
TY  - JOUR
AU  - M. V. Bondarko
TI  - The generic fibre of finite group schemes; a ``finite wild'' criterion for good reduction of Abelian varieties
JO  - Izvestiya. Mathematics 
PY  - 2006
SP  - 661
EP  - 691
VL  - 70
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2006_70_4_a1/
LA  - en
ID  - IM2_2006_70_4_a1
ER  - 
%0 Journal Article
%A M. V. Bondarko
%T The generic fibre of finite group schemes; a ``finite wild'' criterion for good reduction of Abelian varieties
%J Izvestiya. Mathematics 
%D 2006
%P 661-691
%V 70
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2006_70_4_a1/
%G en
%F IM2_2006_70_4_a1
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