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On the l-adic representations attached to simple abelian varieties of type IV

Published online by Cambridge University Press:  17 April 2009

Wenchen Chi
Wenchen Chi
Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China
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Abstract

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The l-adic representations associated to prime dimensional type IV absolutely simple abelian varieties over number fields are studied. The image of such a representation was computed. The results coincide with the well-known conjectures of Mumford and Tate.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 1 , August 1991 , pp. 71 - 78
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Bogomolov, F.A., ‘Sur l'algébricité des représentations l–adiques’, C.R. Acad. Sc. Paris, 290 (1980), 701–703.Google Scholar
[2]Chi, W., ‘On the l–adic representations attached to some absolutely simple abelian varieties of type II’, J. Fac. Sci. Univ. Tokyo. Sect. IA Math. (1990) (to appear).Google Scholar
[3]Deligne, P., Hodge cycles on Abelian varieties (notes by J.S. Milne): Lecture Notes in Math. 900, pp. 9–100 (Springer-Verlag, Berlin, Heidelberg, New York, 1982).CrossRefGoogle Scholar
[4]Faltings, G., ‘Endlichkeitssätze fur abelsche varietäten uber zahlkörpern’, Invent. Math. 73 (1983), 349–366.Google Scholar
[5]Mumford, D., ‘Families of abelian varieties’, in Proc. of Symposia in Pure Math. IX, pp. 347–351 (A.M.S., 1966).CrossRefGoogle Scholar
[6]Mumford, D., Abelian varieties (Oxford University Press, 1974).Google Scholar
[7]Ribet, K., ‘Hodge classes on certain types of abelian varieties’, Amer. J. Math. 105 (1983), 523–538.CrossRefGoogle Scholar
[8]Sen, S., ‘Lie algebras of Galois groups arising from Hodge-Tate modules’, Ann. of Math. 97 (1973), 160–170.CrossRefGoogle Scholar
[9]Serre, J-P., ‘Sur les groupes de Galois attachés aux groupes p–divisibles’, in Proceedings of a Conference on Local Fields, pp. 118–131 (Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[10]Serre, J-P., ‘Groupes algébriques associés aux modules de Hodge-Tate’, Astérisque 65 (1979), 155–188.Google Scholar
[11]Shimura, G. and Taniyama, Y., ‘Complex multiplication of abelian varieties and its applications to number theory’, Publ. Math. Soc. Japan 6 (1961).Google Scholar
[12]Shimura, G., ‘On analytic families of polarized abelian varieties and automorphic functions’, Ann. of Math. 78 (1963), 149–192.CrossRefGoogle Scholar
[13]Tanke’ev, S.G., ‘Algebraic cycles on simple 5-dimensional abelian varieties’, Math. USSR Izv. 19 (1982), 95–123.CrossRefGoogle Scholar
[14]Tanke’ev, S.G., ‘Cycles on simple abelian varieties of prime dimension’, Math. USSR Izv. 20 (1983), 157–171.CrossRefGoogle Scholar
[15]Tate, J., Algebraic cycles and poles of zeta functions, Arithmetical algebraic geometry, pp. 93–110 (Harper and Row, New York, 1965).Google Scholar
[16]Tate, J., ‘p–divisible groups’, in Proc. of a Conference on Local Fields, pp. 158–183 (Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar