Connectedness results for ℓ-adic representations associated to abelian varieties
Silverberg, A. ; Zarhin, Yu G.
Compositio Mathematica, Tome 99 (1995), p. 273-284 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1995-01-01
@article{CM_1995__97_1-2_273_0,
     author = {Silverberg, Alice and Zarhin, Yuri},
     title = {Connectedness results for $\ell $-adic representations associated to abelian varieties},
     journal = {Compositio Mathematica},
     volume = {99},
     year = {1995},
     pages = {273-284},
     mrnumber = {1355128},
     zbl = {1044.11586},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1995__97_1-2_273_0}
}

Silverberg, A.; Zarhin, Yu G. Connectedness results for $\ell $-adic representations associated to abelian varieties. Compositio Mathematica, Tome 99 (1995) pp. 273-284. http://gdmltest.u-ga.fr/item/CM_1995__97_1-2_273_0/

1 F.A. Bogomolov, Sur l'algébricité des représentations l-adiques, C.R.A.S. Paris 290 (1980) 701-703. | Zbl 0457.14020

2 A. Borel, Linear Algebraic Groups (Second Enlarged Edition), Springer-Verlag, New York, 1991. | MR 1102012 | Zbl 0726.20030

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. | MR 352101 | Zbl 0326.14013

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. | MR 548334 | Zbl 0417.14028

5 W. Chi, l-adic and λ-adic representations associated to abelian varieties defined over number fields, Amer. J. Math. 114 (1992) 315-353. | Zbl 0795.14024

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 Mathematics 900, Springer-Verlag, Berlin-Heidelberg-New York, 1982, pp. 9-100. | Zbl 0537.14006

7 G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983) 349-366. | MR 718935 | Zbl 0588.14026

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. | MR 766568

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. | MR 354656 | Zbl 0248.14006

10 J.E. Humphreys, Linear Algebraic Groups, Graduate Texts in Mathematics 21, Springer-Verlag, New York- Heidelberg-Berlin, 1975. | MR 396773 | Zbl 0325.20039

11 L. Moret-Bailly, Pinceaux de Variétés Abéliennes, Astérisque 129 (1985). | MR 797982 | Zbl 0595.14032

12 S. Mori, On Tate conjecture concerning endomorphisms of abelian varieties, in Proceedings of the International Symposium on Algebraic Geometry, Kyoto 1977 (M. Nagata, ed.), Kinokuniya Book-store Co., Ltd., Tokyo, 1978. | MR 578861 | Zbl 0421.14007

13 I.I. Piatetski-Shapiro, Interrelations between the Tate and Hodge conjectures for abelian varieties (Russian), Mat. Sbornik 85 (1971) 610-620 = Math. USSR Sbornik 14 (1971) 615-625. | MR 294352 | Zbl 0239.14019

14 K. Ribet, Hodge classes on certain types of abelian varieties, Amer. J. Math. 105 (1983) 523-538. | MR 701568 | Zbl 0586.14003

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. | MR 476753 | Zbl 0406.14015

16 J.-P. Serre, Letters to K. Ribet, Jan. 1, 1981 and Jan. 29, 1981.

17 J.-P. Serre, Résumé des cours de 1985-1986, Collège de France.

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. | MR 1265537 | Zbl 0812.14002

19 A. Silverberg, Fields of definition for homomorphisms of abelian varieties, J. Pure and Applied Algebra 77 (1992) 253-262. | MR 1154704 | Zbl 0808.14037

20 A. Silverberg, Yu. G. Zarhin, Isogenies of abelian varieties, J. Pure and Applied Algebra 90 (1993) 23-37. | MR 1246271 | Zbl 0832.14034

21 A. Silverberg, Yu. G. Zarhin, Variations on a theme of Minkowski and Serre, to appear in J. Pure and Applied Algebra. | MR 1394358 | Zbl 0885.14006

22 A. Silverberg, Yu. G. Zarhin, Semistable reduction and torsion subgroups of abelian varieties, to appear in Ann. Inst. Fourier 45, 2 (1995). | Numdam | MR 1343556 | Zbl 0818.14017

23 A. Weil, Variétés abéliennes et courbes algébriques, Hermann, Paris, 1948. | MR 29522 | Zbl 0037.16202

24 A. Well, Basic Number Theory, Springer-Verlag, Berlin-Heidelberg-New York, 1967. | Zbl 0176.33601

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. | MR 371897 | Zbl 0345.14014

26 Yu. G. Zarhin, Abelian varieties in characteristic p (Russian), Mat. Zametki 19 (1976) 393-400 Math. Notes 19 (1976) 240-244. | MR 422287 | Zbl 0342.14011

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. | MR 740792 | Zbl 0579.14019

28 Yu. G. Zarhin, A.N. Parshin, Finiteness problems in Diophantine Geometry, Amer. Math. Soc. Transl. 143 (1989) 35-102. | Zbl 0672.14012