Geodesic
Honda systems of group schemes of period~$p$
Izvestiya. Mathematics , Tome 30 (1988) no. 3, pp. 419-453.

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

A direct construction is given of the Fontaine anti-equivalence between the subcategories of finite commutative group schemes over the ring of Witt vectors and of finite Honda systems in the case of objects annihilated by multiplication by $p$ (for $p=2$ there is no restriction involving the unipotency of the corresponding objects). An explicit description of the algebras of group schemes of the category under consideration is obtained and it is shown that the bifunctor $\operatorname{Ext}^2$ in this category is identically equal to zero. Bibliography: 11 titles. 
@article{IM2_1988_30_3_a0,
     author = {V. A. Abrashkin},
     title = {Honda systems of group schemes of period~$p$},
     journal = {Izvestiya. Mathematics },
     pages = {419--453},
     publisher = {mathdoc},
     volume = {30},
     number = {3},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1988_30_3_a0/}
}
TY  - JOUR
AU  - V. A. Abrashkin
TI  - Honda systems of group schemes of period~$p$
JO  - Izvestiya. Mathematics 
PY  - 1988
SP  - 419
EP  - 453
VL  - 30
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1988_30_3_a0/
LA  - en
ID  - IM2_1988_30_3_a0
ER  - 
%0 Journal Article
%A V. A. Abrashkin
%T Honda systems of group schemes of period~$p$
%J Izvestiya. Mathematics 
%D 1988
%P 419-453
%V 30
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1988_30_3_a0/
%G en
%F IM2_1988_30_3_a0
V. A. Abrashkin. Honda systems of group schemes of period~$p$. Izvestiya. Mathematics , Tome 30 (1988) no. 3, pp. 419-453. http://geodesic.mathdoc.fr/item/IM2_1988_30_3_a0/

[1] Fontaine J.-M., “Groupes finis commutatifs sur les vecteurs de Witt”, C.R. Acad. Sci., 280 (1975), A1423–A1425 | MR

[2] Fontaine J.-M., Groupes $p$-divisibles sur les corps locaux, Soc. Math. de France. Paris, Asterisque, 47,48, 1977 | MR | Zbl

[3] Fontaine J.-M., “Sur la construction du module de Dieudonne d'un groupe formel”, C.R. Acad. Sci., 280 (1975), A1273–A1276 | MR

[4] Demazure M., Gabriel P., Groupes algebriques, v. 1, North Holland Publ. Co., Amsterdam, 1970 | MR

[5] Raynaud M., “Schemas en groupes ty dype $(p,\dots,p)$”, Bull. Soc. Math. France, 102 (1974), 248–280 | MR

[6] Teit Dzh., Oort F., “Skhemy grupp prostogo poryadka”, Matematika, 16:1 (1972), 165–183 | MR

[7] Abrashkin V. A., “Khoroshaya reduktsiya abelevykh mnogoobrazii”, Izv. AN SSSR. Ser. matem., 40:2 (1976), 262–272 | MR | Zbl

[8] Dzhekobson N., Teoriya kolets, IL, M., 1985

[9] Fontaine J.-M., Il n'y a pas de variete abelienne sur $\mathbf{Z}$, Prepublication de l'Institut Fourier No 21, 1984

[10] Abrashkin V. A., “Gruppovye skhemy perioda $p$ nad koltsom vektorov Vitta”, Dokl. AN SSSR, 283:6 (1985), 1289–1294 | MR | Zbl

[11] Berthelote P., “Systemes de Honda des schemas en $\mathbf{F}_q$-vectoriels”, Bull. Soc. Math. France, 105 (1977), 225–239 | MR