Geodesic
K3 surfaces over number fields and the Mumford--Tate conjecture
Izvestiya. Mathematics , Tome 37 (1991) no. 1, pp. 191-208.

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Given a K3 surface $S$ over a number field $k$, the author computes the semisimple part of the Lie algebra of the image of the $l$-adic representation in 2-dimensional cohomology of $S$ under the condition that $\operatorname{rank}NS(S\otimes_k\bar k)\ne2$. 
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S. G. Tankeev. K3 surfaces over number fields and the Mumford--Tate conjecture. Izvestiya. Mathematics , Tome 37 (1991) no. 1, pp. 191-208. http://geodesic.mathdoc.fr/item/IM2_1991_37_1_a7/

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

[2] Borevich Z. I., Shafarevich I. R., Teoriya chisel, Nauka, M., 1985 | MR | Zbl

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

[4] Zarhin Yu. G., “Abelian varieties, $l$-adic representations and Lie algebras. Rank independence on $l$”, Invent. Math., 55 (1979), 165–176 | DOI | MR

[5] Kostant B., “A characterization of the classical groups”, Duke Math. J., 25 (1958), 107–123 | DOI | MR | Zbl

[6] Leng S., Algebraicheskie chisla, Mir, M., 1966 | MR

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

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

[9] Serre J.-P., “Representations $l$-adiques”, Algebraic number theory. Papers contributed, Kyoto Internat. Sympos., Res. Inst. Math. Sci., Univ. Kyoto (Kyoto, 1976), Japan Soc. Promotion Sci., Tokyo, 1977, 177–193 | MR

[10] Serre J.-P., “Resumé des cours de 1984–85”, Annuaire du Collège de France, 1985, 1–8 | MR

[11] Serre J.-P., “Groupes algébriques associés aux modules de Hodge–Tate”, Astérisques, 65, 1979, 155–188 | MR

[12] Cepp Zh.-P., Kurs arifmetiki, Mir, M., 1972 | MR

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

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

[15] Tankeev S. G., “Tsikly na prostykh abelevykh mnogoobraziyakh prostoi razmernosti nad chislovymi polyami”, Izv. AN SSSR. Ser. matem., 51:6 (1987), 1214–1227 | MR

[16] Tankeev S. G., “Poverkhnosti tipa K3 nad chislovymi polyami i $l$-adicheskie predstavleniya”, Izv. AN SSSR. Ser. matem., 52:6 (1988), 1252–1271