Geodesic
Cycles on simple Abelian varieties of prime dimension over number fields
Izvestiya. Mathematics , Tome 31 (1988) no. 3, pp. 527-540.

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

For all simple Abelian varieties of prime dimension over number fields the author proves 1) a version of the Mumford–Tate conjecture, asserting that the Lie algebra of the image of the $l$-adic representation is isomorphic to the Lie algebra of the set of $\mathbf Q_l$-points of the Mumford–Tate group, and 2) the Tate conjecture on cycles. Bibliography: 21 titles. 
@article{IM2_1988_31_3_a4,
     author = {S. G. Tankeev},
     title = {Cycles on simple {Abelian} varieties of prime dimension over number fields},
     journal = {Izvestiya. Mathematics },
     pages = {527--540},
     publisher = {mathdoc},
     volume = {31},
     number = {3},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1988_31_3_a4/}
}
TY  - JOUR
AU  - S. G. Tankeev
TI  - Cycles on simple Abelian varieties of prime dimension over number fields
JO  - Izvestiya. Mathematics 
PY  - 1988
SP  - 527
EP  - 540
VL  - 31
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1988_31_3_a4/
LA  - en
ID  - IM2_1988_31_3_a4
ER  - 
%0 Journal Article
%A S. G. Tankeev
%T Cycles on simple Abelian varieties of prime dimension over number fields
%J Izvestiya. Mathematics 
%D 1988
%P 527-540
%V 31
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1988_31_3_a4/
%G en
%F IM2_1988_31_3_a4
S. G. Tankeev. Cycles on simple Abelian varieties of prime dimension over number fields. Izvestiya. Mathematics , Tome 31 (1988) no. 3, pp. 527-540. http://geodesic.mathdoc.fr/item/IM2_1988_31_3_a4/

[1] Dzh. Kassels, A. Frelikh (red.), Algebraicheskaya teoriya chisel, Mir, M., 1969

[2] Burbaki N., Gruppy i algebry Li, gl. 1–3, Mir, M., 1976 ; гл. 4–6, 1972 ; гл. 7–8, 1978 | MR | Zbl

[3] Faltings G., “Endlichkeitssätze fur abelsche Varietäten über Zahlkörpern”, Invent. Math., 73 (1983), 349–366 | DOI | MR | Zbl

[4] Hodge W. V. D., “The topological invariants of algebraic varieties”, Proc. Inter. Cong., v. 1, Camb. Mass., 1950, 182–192 | MR

[5] Zarkhin Yu. G., “Kruchenie abelevykh mnogoobrazii v konechnoi kharakteristike”, Matem. zametki, 22:1 (1977), 3–11 | Zbl

[6] Zarkhin Yu. G., Kogomologii algebraicheskikh mnogoobrazii i predstavleniya poluprostykh algebr Li, Preprint NTsBI AN SSSR, Puschino, 1980 | Zbl

[7] Zarkhin Yu. G., “Abelevy mnogoobraziya, $l$-adicheskie predstavleniya i $SL_2$”, Izv. AN SSSR. Ser. matem., 43:2 (1979), 294–308 | MR | Zbl

[8] Zarhin Yu. G., “Hodge groups of K3 surfaces”, J. für die Reine und Angew. Math., 341 (1983), 193–220 | MR

[9] Zarhin Yu. G., “Abelian varieties, $l$-adic representations and Lie algebras. Rank independence on $l$”, Invent. Math., 55 (1979), 166–176 | DOI | MR

[10] Mumford D., “Families of abelian varieties. Algebraic groups and discontinuous subgroups”, Proc. Symp. in Pure Math., 9 (1966), 347–352 | MR

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

[12] Pyatetskii-Shapiro I. I., “Vzaimootnosheniya mezhdu gipotezami Teita i Khodzha dlya abelevykh mnogoobrazii”, Matem. sb., 85(127):4(8) (1971), 610–620

[13] Serr Zh.-P., Abelevy $l$-adicheskie predstavleniya i ellipticheskie krivye, Mir, M., 1973 | Zbl

[14] Serre J.-P., “Representations $l$-adiques”, Algebraic number theory, Papers contributed for the International Symposium (Kyoto, 1976), ed. S. Iyanaga, Japan Society for the Promotion of Science, Tokyo, 1977, 177–193 | MR

[15] Tate J., “Algebraic cycles and poles of zeta functions”, Arithmetical Algebraic Geometry, New York, 1966, 93–110 | MR

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

[17] Teit Dzh., “Klassy izogenii abelevykh mnogoobrazii nad konechnymi polyami”, Matematika, 14:6 (1970), 129–137

[18] Tankeev S. G., “Ob algebraicheskikh tsiklakh na poverkhnostyakh i abelevykh mnogoobraziyakh”, Izv. AN SSSR. Ser. matem., 45:2 (1981), 398–434 | MR | Zbl

[19] Tankeev S. G., “Ob algebraicheskikh tsiklakh na prostykh 5-mernykh abelevykh mnogoobraziyakh”, Izv. AN SSSR. Ser. matem., 45:4 (1981), 793–823 | MR

[20] Tankeev S. G., “Tsikly na prostykh abelevykh mnogoobraziyakh prostoi razmernosti”, Izv. AN SSSR. Ser. matem., 46:1 (1982), 155–170 | MR

[21] Bogomolov F. A., “Tochki konechnogo poryadka na abelevom mnogoobrazii”, Izv. AN SSSR. Ser. matem., 44:4 (1980), 782–804 | MR | Zbl