Points of finite order on an Abelian variety
Izvestiya. Mathematics , Tome 17 (1981) no. 1, pp. 55-72.

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

In this paper it is shown that the image of the Galois group under an $l$-adic representation in the Tate module of an Abelian variety has an algebraic Lie algebra which contains the scalar matrices as a subalgebra (Serre's conjecture). This paper also proves the finiteness of the intersection of a subgroup of an Abelian variety all of whose elements have order equal to a power of a fixed number with a wide class of subvarieties. Bibliography: 13 titles.
@article{IM2_1981_17_1_a1,
     author = {F. A. Bogomolov},
     title = {Points of finite order on an {Abelian} variety},
     journal = {Izvestiya. Mathematics },
     pages = {55--72},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {1981},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1981_17_1_a1/}
}
TY  - JOUR
AU  - F. A. Bogomolov
TI  - Points of finite order on an Abelian variety
JO  - Izvestiya. Mathematics 
PY  - 1981
SP  - 55
EP  - 72
VL  - 17
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1981_17_1_a1/
LA  - en
ID  - IM2_1981_17_1_a1
ER  - 
%0 Journal Article
%A F. A. Bogomolov
%T Points of finite order on an Abelian variety
%J Izvestiya. Mathematics 
%D 1981
%P 55-72
%V 17
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1981_17_1_a1/
%G en
%F IM2_1981_17_1_a1
F. A. Bogomolov. Points of finite order on an Abelian variety. Izvestiya. Mathematics , Tome 17 (1981) no. 1, pp. 55-72. http://geodesic.mathdoc.fr/item/IM2_1981_17_1_a1/

[1] Manin Yu. I., “Tonkaya struktura vysoty Nerona–Teita”, Matem. sb., 83:3 (1970), 331–348 | MR | Zbl

[2] Mumford D., “A remark on Mordells conjecture”, Amer. J. Math., 87 (1965), 1007–1016 | DOI | MR | Zbl

[3] Mumford D., Abelien varieties, Bombay, 1968; Mamford D., Abelevy mnogoobraziya, Mir, M., 1971

[4] Lang S., Diophantine geometry, Interscience Tracts in Pure and Applied Mathematics, No 11, Interscience Publishers (a division of John Wiley and Sons), New York, London, 1962 | MR

[5] Lang S., “Division points on curves”, Ann. Mat. Pura Appl.(4), 70 (1965), 229–234 | DOI | MR | Zbl

[6] Sen S., “Lie algebras of Galois groups arising from Hodge–Tate modules”, Ann. of Math., 97 (1973), 160–170 | DOI | MR | Zbl

[7] Serre J.-P., “Sur les groupes de congruence des variétés abeliennes”, Izv. AN SSSR. Ser. matem., 28 (1964), 3–20 | MR

[8] Serre J.-P., “Sur les groupes de Galois attachés aux groupes $p$-divisibles”, Proceedings of Conference on “Local fileds”, Springer-Verlag, 1967, 118–131 | MR

[9] Serre J.-P., Abelian $l$-adic representations and elliptic curves, McGill University lecture notes written with the collaboration of Willem Kuyk and John Labute, Benjamin, New York, 1968 ; Serr Zh.-P., Abelevy $l$-adicheskie predstavleniya i ellipticheskie krivye, Mir, M., 1973 | MR | Zbl | Zbl

[10] Tate J., “$p$-divisible groupes”, Proceedings of Conference on “Local fields”, Springer-Verlag, 1967, 158–183 | MR

[11] Lang S., “Some theorems and conjectures in diophantine equations”, Bull. Amer. Math. Soc., 66:4 (1960), 240–249 | DOI | MR | Zbl

[12] Chevalley C., Theory of Lie groups, t. III, Publ. de lTnstitut math. de l'univ. de Nancago, Paris, 1955 ; Shevalle K., Teoriya grupp Li, t. III, IIL, M., 1958 | Zbl

[13] Serre J.-P., “Representations $l$-adiques”, Algebraic number theory (Int. Symp., Kyoto), 1976 | MR