Pairs of mod 3 and mod 5 representations arising from elliptic curves

Mathematical Research Letters

Volumn 6, Issue 5-6, 1999, Pages 735-754

  Manoharmayum, J ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033235859     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/mrl.1999.v6.n6.a12     Document Type: Article

References (20)

1. [CDT] B. Conrad, F. Diamond, and R. Taylor, Modularity of certain potentially Barsotti-Tate Galois representations. J. Amer. Math. Soc. 12 (1999), 521-567.
2. [Dia] F. Diamond, On deformation rings and Hecke rings, Ann. of Math. (2) 144 (1996), 137-166.
3. [D-K] F. Diamond and K. Kramer, Classification of ρ̄E,l by j invariant of E, In Modular forms and Fermat's last theorem (Boston, MA, 1995), pp. 491-498, Springer-Verlag, New York, 1997.
4. [Hon] T. Honda, Isogeny classes of abelian varieties over finite fields, J. Math. Soc. Japan 20 (1968), 83-95.
5. [Ka-Ma] N.M. Katz and B. Mazur, Arithmetic moduli of elliptic curves, Annals of Mathematics Studies 108, Princeton University Press, Princeton, 1985.
6. [Kis1] M. Kisin, Local constancy in p-adic families of Galois representations, preprint.
7. [Kis2] _, Local constancy in p-adic families of Galois representations, Princeton University Ph.D. thesis.
8. [R-S] K. Rubin and A. Silverberg, Families of elliptic curves with constant mod p representations, in Elliptic Curves, Modular Forms, & Fermat's Last Theorem (Hong Kong, 1993), pp. 148-161, Ser. Number Theory, I, Internat. Press, Cambridge, MA, 1995.
9. [SB-T] N.I. Shepherd-Barron and R. Taylor, Mod 2 and mod 5 icosahedral representations, J. Amer. Math. Soc. 10 (1997), 283-298.
10. [Se1] J.-P. Serre, Abelian l-adic representations and elliptic curves, W.A. Benjamin, Inc., New York, 1968.
11. [Se2] _, A course in arithmetic, Graduate Texts in Mathematics, No. 7. Springer-Verlag, New York, 1973.
12. [Se3] _, Propriétés Galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math. 15 (1972), 259-331.
13. [Shi] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Princeton Univ. Press, Princeton, N.J., 1971.
14. [Si] A. Silverberg, Explicit families of elliptic curves with prescribed mod N representations, in Modular forms and Fermat's last theorem, (Boston, MA, 1995), pp. 447-461, Springer-Verlag, New York, 1997.
15. [Sil1] J. Silverman, The arithmetic of elliptic curves, Graduate Texts in Mathematics, 106. Springer-Verlag, New York, 1986.
16. [Sil2] _, Advanced topics in the arithmetic of elliptic curves, Graduate Texts in Mathematics, 151. Springer-Verlag, New York, 1994.
17. [Ta] J. Tate, Classes d'isogénie des variétes abéliennes sur un corps fini (d'après T. Honda), Seminaire Bourbaki 352 (1968).
18. [T-W] R. Taylor and A. Wiles, Ring theoretic properties of certain Hecke algebras, Ann. of Math (3) 141 (1995), 553-572.
19. [v-Wa] B.L. van der Waerden, Algebra, Volume 1, Springer-Verlag, New York, 1991.
20. [Wi] A. Wiles, Modular elliptic curves and Fermat's last theorem, Annals of Math (3) 141 (1995), 443-551.