On certain Galois representations related to the modular curve X 1 ( p )

Ehud De Shalit

Compositio Mathematica (1995)

  • Volume: 95, Issue: 1, page 69-100
  • ISSN: 0010-437X

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De Shalit, Ehud. "On certain Galois representations related to the modular curve $X_1(p)$." Compositio Mathematica 95.1 (1995): 69-100. <http://eudml.org/doc/90345>.

@article{DeShalit1995,
author = {De Shalit, Ehud},
journal = {Compositio Mathematica},
keywords = {modular forms; Hecke algebras; Tate -adic period; Mazur-Tate conjecture; modular elliptic curve; -adic unit; -adic logarithm; deformations of Galois representations; exceptional zero conjecture},
language = {eng},
number = {1},
pages = {69-100},
publisher = {Kluwer Academic Publishers},
title = {On certain Galois representations related to the modular curve $X_1(p)$},
url = {http://eudml.org/doc/90345},
volume = {95},
year = {1995},
}

TY - JOUR
AU - De Shalit, Ehud
TI - On certain Galois representations related to the modular curve $X_1(p)$
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 95
IS - 1
SP - 69
EP - 100
LA - eng
KW - modular forms; Hecke algebras; Tate -adic period; Mazur-Tate conjecture; modular elliptic curve; -adic unit; -adic logarithm; deformations of Galois representations; exceptional zero conjecture
UR - http://eudml.org/doc/90345
ER -

References

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  1. [A] Artin, M.Néron models, in: G. Cornell and J. Silverman (eds.) Arithmetic Geometry, Springer-Verlag, New York (1986). MR861969
  2. [B-L-R] Bosch, S., Lutkebohmert, W. and Raynaud, M., Néron Models. Springer-Verlag. Zbl0705.14001MR1045822
  3. [dS1] de Shalit, E., Kronecker's polynomial, supersingular elliptic curves, and p-adic periods of modular curves. Contemp. Math.165, AMS (1994), 135-148. Zbl0863.14015
  4. [dS2] de Shalit, E., P-adic periods and modular symbols of elliptic curves of prime conductor. To appear in Invent. Math. Zbl1044.11576MR1346205
  5. [dS3] de Shalit, E., On the p-adic periods of X0(p). To appear in Math. Ann. Zbl0864.14014MR1355000
  6. [G-S] Greenberg, R. and Stevens, G., P-adic L functions and p-adic periods of modular forms, Invent. Math.111 (1993) 407-447. Zbl0778.11034MR1198816
  7. [Gr] Gross, B., Heights and special values of L series, Proceedings of the 1985 Montreal conference in Number Theory. CMS conference proceedings, vol. 7. Zbl0623.10019
  8. [Groth] Grothendieck, A., Modeles de néron et monodromie, in: SGA 71, LNM288, Springer-Verlag (1972). Zbl0248.14006MR354656
  9. [Hi] Hida, H., Galois representations into GL2(Zp[[X]]) attached to ordinary cusp forms, Inv. Math.85 (1986) 543-613. Zbl0612.10021MR848685
  10. [K-M] Katz, N. and Mazur, B., Arithmetic moduli of elliptic curves, Ann. Math. Stud.108. Princeton (1985). Zbl0576.14026
  11. [M-D] Manin, J. and Drinfeld, V.G., Periods of p-adic Schottky groups, J.f.d. reine u. angew. Math.262/3 (1973) 239-247. Zbl0275.14017MR396582
  12. [M] Mazur, B., Modular curves and the Eisenstein ideal. Publ. Math. I.H.E.S.47 (1977) 33-186. Zbl0394.14008MR488287
  13. [M-T] Mazur, B. and Tate, J., Refined conjectures of the "Birch and Swinnerton-Dyer type", Duke Math. J.54 (1987) 711-750. Zbl0636.14004MR899413
  14. [M-T-T] Mazur, B., Tate, J. and Teitelbaum, J., On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer, Inv. Math.84 (1986) 1-48. Zbl0699.14028MR830037
  15. [M-W1] Mazur, B. and Wiles, A., Class fields of abelian extensions of Q, Inv. Math.76 (1984) 179-330. Zbl0545.12005MR742853
  16. [M-W2] Mazur, B. and Wiles, A., On p-adic analytic families of Galois representations, Compositio Math.59 (1986) 231-264. Zbl0654.12008MR860140
  17. [Mi] Milne, J., Etale Cohomology, PUP, Princeton (1980). Zbl0433.14012MR559531
  18. [Se] Serre, J.-P., Groupes Algébriques et Corps de Classes, Hermann, Paris (1959). Zbl0097.35604
  19. [W] Wiles, A., Modular curves and the class group of Q(ζp), Inv. Math.58 (1980) 1-35. Zbl0436.12004

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