Geodesic
Surfaces of type~K3 over number fields and the Mumford--Tate conjecture.~II
Izvestiya. Mathematics , Tome 59 (1995) no. 3, pp. 619-646.

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

The Mumford–Tate conjecture is proved for any smooth projective surface of type K3 over a number field. 
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S. G. Tankeev. Surfaces of type~K3 over number fields and the Mumford--Tate conjecture.~II. Izvestiya. Mathematics , Tome 59 (1995) no. 3, pp. 619-646. http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a6/

[1] Algebraicheskaya teoriya chisel, eds. Dzh. Kassels, A. Frelikh, Mir, M., 1969 | MR

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

[3] Chi W., “$l$-adic and $\lambda $-adic representations associated to abelian varieties defined over number fields”, Amer. J. Math., 114 (1992), 315–353 | DOI | MR | Zbl

[4] Deligne P., “La conjecture de Weil pour les surfaces K3”, Invent. math., 15 (1972), 206–226 | DOI | MR | Zbl

[5] Zarkhin Yu. G., “Abelevy mnogoobraziya, $l$-adicheskie predstavleniya i $\operatorname {SL}_2$”, Izv. AN SSSR. Ser. matem., 43:2 (1979), 294–308 | MR | Zbl

[6] Zarhin Yu. G., “Hodge groupes of K3 surfaces”, J. für die reine und angew. Math., 341 (1983), 193–220 | 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] Serr Zh.-P., Algebry Li i gruppy Li, Mir, M., 1969 | MR | Zbl

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

[11] Tate J., “Classes d'isogénie des variétés abéliennes sur un corps fini (d'après T. Honda)”, Séminaire Bourbaki 1968/69, Expose 352, Lecture Notes in Math., 179, 1971, 95–110

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

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

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

[15] Tankeev S. G., “Poverkhnosti tipa K3 nad chislovymi polyami i gipoteza Mamforda–Teita”, Izv. AN SSSR. Ser. matem., 54:4 (1990), 846–861

[16] Tankeev S. G., “Abelevy mnogoobraziya Kugi–Satake i $l$-adicheskie predstavleniya”, Izv. AN SSSR. Ser. matem., 55:4 (1991), 877–889 | Zbl

[17] Tankeev S. G., “Algebraicheskie tsikly na abelevom mnogoobrazii bez kompleksnogo umnozheniya”, Izv. RAN. Ser. matem., 58:3 (1994), 103–126 | MR | Zbl

[18] Pyatetskii-Shapiro I. I., Shafarevich I. R., “Arifmetika poverkhnostei tipa K3”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 132 (1973), 44–54 | MR

[19] Borovoi M. V., “Skhemy Shimury–Delinya $M_{\mathbb C}(G,h)$ i ratsionalnye klassy kogomologii tipa $(p,p)$ abelevykh mnogoobrazii”, Voprosy teorii grupp i gomologicheskoi algebry, no. 1, Izd-vo YarGU, Yaroslavl, 1977, 3–53 | MR

[20] Mumford D., “A note on paper: Shimura, Discontinuous groups and abelian varieties”, Math. Ann., 181:4 (1969), 345–351 | DOI | MR | Zbl