Connectedness results for $l$-adic representations associated to abelian varieties

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1. 1 F.A. Bogomolov, Sur l'algébricité des représentations l-adiques, C.R.A.S. Paris290 (1980) 701-703. Zbl0457.14020
2. 2 A. Borel, Linear Algebraic Groups (Second Enlarged Edition), Springer-Verlag, New York, 1991. Zbl0726.20030MR1102012
3. 3 M. Borovoi, The action of the Galois group on the rational cohomology classes of type (p, p) of abelian varieties (Russian), Mat. Sbornik (N. S.) 94 (136) (1974) 649-652 = Math. USSR Sbornik 23 (1974) 613-616. Zbl0326.14013MR352101
4. 4 M. Borovoi, The Shimura-Deligne schemes Mc (G, h) and the rational cohomology classes of type (p, p) of abelian varieties (Russian), Problems of group theory and homological algebra, No. 1 (Russian), pp. 3-53, Yaroslav. Gos. Univ., Yaroslavl', 1977. Zbl0417.14028MR548334
5. 5 W. Chi, l-adic and λ-adic representations associated to abelian varieties defined over number fields, Amer. J. Math. 114 (1992) 315-353. Zbl0795.14024
6. 6. Deligne (notes by J. Milne), Hodge cycles on abelian varieties, in Hodge cycles, motives, and Shimura varieties ( P. Deligne, J. Milne, A. Ogus, K.-Y. Shih), Lecture Notes in Mathematics900, Springer-Verlag, Berlin-Heidelberg-New York, 1982, pp. 9-100. Zbl0537.14006
7. 7 G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math.73 (1983) 349-366. Zbl0588.14026MR718935
8. 8 G. Faltings, Complements to Mordell, Chapter VI of Rational Points (G. Faltings, G. Wüstholz, et al.) (Third Enlarged Edition), Friedr. Vieweg & Sohn, Braunschweig/ Wiesbaden, 1992. MR766568
9. 9 A. Grothendieck, Modèles de Néron et monodromie, in Groupes de monodromie en géometrie algébrique, SGA7 I (A. Grothendieck, ed.), Lecture Notes in Math.288, Springer, Berlin-Heidelberg -New York, 1972, pp. 313-523. Zbl0248.14006MR354656
10. 10 J.E. Humphreys, Linear Algebraic Groups, Graduate Texts in Mathematics 21, Springer-Verlag, New York- Heidelberg-Berlin, 1975. Zbl0325.20039MR396773
11. 11 L. Moret-Bailly, Pinceaux de Variétés Abéliennes, Astérisque129 (1985). Zbl0595.14032MR797982
12. 12 S. Mori, On Tate conjecture concerning endomorphisms of abelian varieties, in Proceedings of the International Symposium on Algebraic Geometry, Kyoto1977 (M. Nagata, ed.), Kinokuniya Book-store Co., Ltd., Tokyo, 1978. Zbl0421.14007MR578861
13. 13 I.I. Piatetski-Shapiro, Interrelations between the Tate and Hodge conjectures for abelian varieties (Russian), Mat. Sbornik85 (1971) 610-620 = Math. USSR Sbornik 14 (1971) 615-625. Zbl0239.14019MR294352
14. 14 K. Ribet, Hodge classes on certain types of abelian varieties, Amer. J. Math.105 (1983) 523-538. Zbl0586.14003MR701568
15. 15 J.-P. Serre, Représentations l-adiques, in Algebraic Number Theory (Proceedings of the International Taniguchi Symposium, Kyoto, 1976) (S. Iyanaga, ed.), Japan Society for the Promotion of Science, Tokyo, 1977, pp. 177-193. Zbl0406.14015MR476753
16. 16 J.-P. Serre, Letters to K. Ribet, Jan. 1, 1981 and Jan. 29, 1981. 
17. 17 J.-P. Serre, Résumé des cours de 1985-1986, Collège de France. 
18. 18 J.-P. Serre, Propriétés conjecturales des groupes de Galois motiviques et des représentations l-adiques, in Motives (U. Jannsen, S. Kleiman, J.-P. Serre, eds.), Proc. Symp. Pure Math 55 (1994), Part 1, pp. 377-400. Zbl0812.14002MR1265537
19. 19 A. Silverberg, Fields of definition for homomorphisms of abelian varieties, J. Pure and Applied Algebra77 (1992) 253-262. Zbl0808.14037MR1154704
20. 20 A. Silverberg, Yu. G. Zarhin, Isogenies of abelian varieties, J. Pure and Applied Algebra90 (1993) 23-37. Zbl0832.14034MR1246271
21. 21 A. Silverberg, Yu. G. Zarhin, Variations on a theme of Minkowski and Serre, to appear in J. Pure and Applied Algebra. Zbl0885.14006MR1394358
22. 22 A. Silverberg, Yu. G. Zarhin, Semistable reduction and torsion subgroups of abelian varieties, to appear in Ann. Inst. Fourier45, 2 (1995). Zbl0818.14017MR1343556
23. 23 A. Weil, Variétés abéliennes et courbes algébriques, Hermann, Paris, 1948. Zbl0037.16202MR29522
24. 24 A. Well, Basic Number Theory, Springer-Verlag, Berlin-Heidelberg-New York, 1967. Zbl0176.33601
25. 25 Yu. G. Zarhin, Endomorphisms of abelian varieties over fields offinite characteristic (Russian), Izv. Akad. Nauk SSSR Ser. Mat.39 (1975) 272-277 = Math. USSR - Izv. 9 (1975) 255-260. Zbl0345.14014MR371897
26. 26 Yu. G. Zarhin, Abelian varieties in characteristic p (Russian), Mat. Zametki19 (1976) 393-400Math. Notes19 (1976) 240-244. Zbl0342.14011MR422287
27. 27 Yu. G. Zarhin, Weights of simple Lie algebras in the cohomology of algebraic varieties (Russian), Izv. Akad. Nauk SSSR Ser. Mat.48 (1984) 264-304 = Math. USSR - Izv. 24 (1985) 245-282. Zbl0579.14019MR740792
28. 28 Yu. G. Zarhin, A.N. Parshin, Finiteness problems in Diophantine Geometry, Amer. Math. Soc. Transl.143 (1989) 35-102. Zbl0672.14012