Geodesic
$p$-divisible groups over $\mathbf Z$
Izvestiya. Mathematics, Tome 11 (1977) no. 5, pp. 937-956 
V. A. Abrashkin. $p$-divisible groups over $\mathbf Z$. Izvestiya. Mathematics, Tome 11 (1977) no. 5, pp. 937-956. http://geodesic.mathdoc.fr/item/IM2_1977_11_5_a1/
@article{IM2_1977_11_5_a1,
     author = {V. A. Abrashkin},
     title = {$p$-divisible groups over~$\mathbf Z$},
     journal = {Izvestiya. Mathematics},
     pages = {937--956},
     year = {1977},
     volume = {11},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1977_11_5_a1/}
}
TY  - JOUR
AU  - V. A. Abrashkin
TI  - $p$-divisible groups over $\mathbf Z$
JO  - Izvestiya. Mathematics
PY  - 1977
SP  - 937
EP  - 956
VL  - 11
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/IM2_1977_11_5_a1/
LA  - en
ID  - IM2_1977_11_5_a1
ER  - 
%0 Journal Article
%A V. A. Abrashkin
%T $p$-divisible groups over $\mathbf Z$
%J Izvestiya. Mathematics
%D 1977
%P 937-956
%V 11
%N 5
%U http://geodesic.mathdoc.fr/item/IM2_1977_11_5_a1/
%G en
%F IM2_1977_11_5_a1

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

In this paper it is shown that: a) there do not exist 3-dimensional abelian varieties over $\mathbf Q$ having everywhere good reduction: b) every 2-divisible group over $\mathbf Z$ of height $\leqslant6$ is isogenous to the trivial one; c) for irregular primes $p$ there exist nontrivial $p$-divisible groups over $\mathbf Z$. Bibliography: 6 titles.

[1] Teit Dzh., “$p$-delimye gruppy”, Matematika, 13:2 (1969), 3–25 | MR

[2] Poitou G., “Minorations des discriminantes (d'apres Odlyzko)”, Sem. Bourbaki, 28-e annee, 479, 1975/76 | MR

[3] Abrashkin V. A., “2-delimye gruppy nad $\mathbf{Z}$”, Matem. zametki, 19:5 (1976), 717–726 | MR | Zbl

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

[5] Iwasawa K., Sims Ch. C., “Computation of invariants in the theory of cyclotomic fields”, J. Math. Soc. Japan, 18:1 (1966), 86–96 | MR | Zbl

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