Geodesic
On homomorphisms of Abelian schemes.~II
Izvestiya. Mathematics , Tome 11 (1977) no. 6, pp. 1175-1194.

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

Let $k$ be a field of algebraic functions of one variable over the field $\mathbf C$ of complex numbers, let $S$ be the complete smooth model of $k$ over $\mathbf C$, and let $\mathscr I_i\to S$ ($i=1,2$) be the Néron models of Abelian varieties $I_i$ over $k$. Suppose that one of the following conditions holds: 1) The minimal models $\mathscr I_i\to S$ admit compactifications whose degenerate fibers are unions of normally crossing smooth irreducible components, and $$ H^0(S,\mathscr Lie_S(\mathscr I_1)\otimes_{\mathscr O_S}\mathscr Lie_S(\mathscr I_2))=(0). $$ 2) The Abelian variety $I_1$ has totally degenerate reduction at a point $v$ of $k$, i.e. the algebraic group $\mathscr I_{1v}$ is an extension of a finite group by a torus. Then for every prime number $l$ the canonical map $$ \operatorname{Hom}_k(I_1,I_2)\otimes_\mathbf Z\mathbf Z_l\to\operatorname{Hom}_{\operatorname{Gal}(\bar k/k)}(T_l(I_1),T_l(I_2)) $$ is an isomorphism. Bibliography: 17 titles. 
@article{IM2_1977_11_6_a2,
     author = {S. G. Tankeev},
     title = {On homomorphisms of {Abelian} {schemes.~II}},
     journal = {Izvestiya. Mathematics },
     pages = {1175--1194},
     publisher = {mathdoc},
     volume = {11},
     number = {6},
     year = {1977},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1977_11_6_a2/}
}
TY  - JOUR
AU  - S. G. Tankeev
TI  - On homomorphisms of Abelian schemes.~II
JO  - Izvestiya. Mathematics 
PY  - 1977
SP  - 1175
EP  - 1194
VL  - 11
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1977_11_6_a2/
LA  - en
ID  - IM2_1977_11_6_a2
ER  - 
%0 Journal Article
%A S. G. Tankeev
%T On homomorphisms of Abelian schemes.~II
%J Izvestiya. Mathematics 
%D 1977
%P 1175-1194
%V 11
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1977_11_6_a2/
%G en
%F IM2_1977_11_6_a2
S. G. Tankeev. On homomorphisms of Abelian schemes.~II. Izvestiya. Mathematics , Tome 11 (1977) no. 6, pp. 1175-1194. http://geodesic.mathdoc.fr/item/IM2_1977_11_6_a2/

[1] Artin M., Grothendieck A., Verdier J.-L., Theorie des topos et cohomologie etale des schemas (SGA-4), tome 3, Lect. Notes Math., 305, Springer-Verlag, 1973 | MR | Zbl

[2] Artin M., “Algebraizatsiya formalnykh modulei”, Matematika, 14:4 (1970), 3–47 | MR | Zbl

[3] Artin M., “Nekotorye chislennye kriterii styagivaemosti krivykh na algebraicheskoi poverkhnosti”, Matematika, 9:3 (1965), 3–14 | MR

[4] Arakelov S. Yu., “Semeistva algebraicheskikh krivykh s fiksirovannymi vyrozhdeniyami”, Izv. AN SSSR. Ser. matem., 35 (1971), 1269–1293 | MR | Zbl

[5] Verde Zh.-L., “Nezavisimost ot $l$-kharakteristicheskogo polinoma endomorfizma Frobeniusa v $l$-adicheskikh kogomologiyakh”, po rabote Delinya, Matematika, 18:2 (1974), 150–161

[6] Delin P., “Teoriya Khodzha, II”, Matematika, 17:5 (1973), 3–56 | MR

[7] Delin P., Mamford D., “Neprivodimost mnogoobraziya krivykh zadannogo roda”, Matematika, 16:3 (1972), 13–53 | Zbl

[8] Deligne P., Grothendieck A., Séminaire de Géométrie Algébrique, preprint, 1968, 1970 | Zbl

[9] Grothendieck A., “Technique de descente et théorèmes d'existence en géométrie algébrique Les schémas de Picard”, Extraits du séminaire Bourbaki, 236, 1957, 1962

[10] Kempf G., Knudsen F., Mumford D., Saint-Donat B., Toroidal embeddings, I, Lect. Notes Math., 339, Springer-Verlag, 1973 | MR | Zbl

[11] Mamford D., Abelevy mnogoobraziya, Mir, M., 1971

[12] Raynaud M., “Spécialisation du foncteur de Picard”, Publ. Math. IHES, 1970, no. 39, 27–76 | MR | Zbl

[13] Raynaud M., “Modèles de Néron”, Comptes Rendus Acad Sci., 262 (1966), 413–416 | MR

[14] Cepp Zh.-P., Teit Dzh., “Khoroshaya reduktsiya abelevykh mnogoobrazii”, Matematika, 15:5 (1971), 140–165

[15] Tate J., “Algebraic cycles and poles of zeta functions”, Arithmetical Algebraic Geometry, New York, 1965, 93–110 | MR | Zbl

[16] Teit Dzh., “Endomorfizmy abelevykh mnogoobrazii nad konechnymi polyami”, Matematika, 12:6 (1968), 31–40

[17] Tankeev S. G., “O gomomorfizmakh abelevykh skhem”, Izv. AN SSSR. Ser. matem., 40 (1976), 774–790 | MR | Zbl