Two-dimensional p -adic Galois representations unramified away from p

B. Mazur

Compositio Mathematica (1990)

  • Volume: 74, Issue: 2, page 115-133
  • ISSN: 0010-437X

How to cite


Mazur, B.. "Two-dimensional $p$-adic Galois representations unramified away from $p$." Compositio Mathematica 74.2 (1990): 115-133. <>.

author = {Mazur, B.},
journal = {Compositio Mathematica},
keywords = {-adic Galois representations; Galois group; newform; Galois representation; non-archimedean valuation; ordinary residual representation; universal deformation; unique cuspidal newform},
language = {eng},
number = {2},
pages = {115-133},
publisher = {Kluwer Academic Publishers},
title = {Two-dimensional $p$-adic Galois representations unramified away from $p$},
url = {},
volume = {74},
year = {1990},

AU - Mazur, B.
TI - Two-dimensional $p$-adic Galois representations unramified away from $p$
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 74
IS - 2
SP - 115
EP - 133
LA - eng
KW - -adic Galois representations; Galois group; newform; Galois representation; non-archimedean valuation; ordinary residual representation; universal deformation; unique cuspidal newform
UR -
ER -


  1. [B1] N. Boston, Explicit deformations of Galois representations. IHES preprint (1988). To appear. Zbl0698.12012MR1079842
  2. [B2] N. Boston, Deformations of Galois representations associated to the cusp form A. IHES preprint (1988). To appear. Zbl0723.11064MR1042764
  3. [B-M] N. Boston and B. Mazur, Explicit universal deformations of Galois representations. Algebraic Number Theory in honor of K. Iwasawa. Advanced Studies in Pure Mathematics series, 17. Academic Press (1989) 1-21. Zbl0739.11021MR1097607
  4. [C-S] J. Coates and C-G. Schmidt, Iwasawa theory for the symmetric square of an elliptic curve. J. Reine Angew. Math.375/376 (1987) 104-156. Zbl0609.14013MR882294
  5. [D] P. Deligne, Formes modulaires et représentations l-adiques. Séminaire Bourbaki68/69 no. 355. Lecture Notes in Mathematics179 pp. 136-172. Springer-Verlag, Berlin-Heidleberg- New York1971. Zbl0206.49901
  6. [D-S] P. Deligne and J.-P. Serre, Formes modulaires de poids 1. Ann. Sci. Ec. Norm. Sup.7 (1974), 507-530 [Republished in J.-P. Serre Oeuvres.Collected Papers Vol. III pp. 193-216, Springer-Verlag, New York-Heidleberg-Berlin- Tokyo1986]. Zbl0321.10026MR379379
  7. [G1] F. Gouvêa, On the ordinary Hecke algebra. IHES Preprint. 1988. To appear. Zbl0774.11026MR1164797
  8. [G2] F. Gouvêa, Arithmetic of p-adic Modular Forms. Lecture Notes in Mathematics1304. Springer Verlag, Berlin-Heidleberg- New York1988. Zbl0641.10024MR1027593
  9. [Gr] B. Gross, The Galois representations associated to modular forms (mod p). Preprint 1988. To appear. 
  10. [H1] H. Hida, Galois representations in GL2(Zp[[X]]) attached to ordinary cusp forms. Inv. Math.85 (1986) 545-613. Zbl0612.10021MR848685
  11. [H2] H. Hida, Iwasawa modules attached to congruences of cusp forms. Ann. Sci. Ec. Norm. Sup.19 (1986) 231-273. Zbl0607.10022MR868300
  12. [M] B. Mazur, Deforming Galois representations. In Y. Ihara, K. Ribet, and J.-P. Serre, eds., Galois Groups over Q, Proceedings of a workshop held at MSRI in March 1987. Springer-Verlag (1989) 385-437. Zbl0714.11076MR1012172
  13. [M-T] B. Mazur and J. Tilouine, Représentations galoisiennes, différentielles de Kähler, et conjectures principales. To appear. Zbl0744.11053
  14. [M-W] B. Mazur and A. Wiles, On p-adic analytic families of Galois representations. Comp. Math.59 (1986) 231-264. Zbl0654.12008MR860140
  15. [Se] J.-P. Serre, Valeurs propres des opérateurs de Hecke modulo l. Journées arith. Bordeaux, Astérisque24-25 (1975),109-117 [Republished in J.-P. Serre Oeuvres.Collected Papers Vol. III pp. 226-234, Springer-VerlagNew YorkHeidlebergBerlinTokyo1986]. Zbl0305.10021MR382173
  16. [Sen 1] S. Sen, Continuous cohomology and p-adic Galois representations. Inv. Math.62 (1980) 87-116. Zbl0463.12005MR595584
  17. [Sen 2] S. Sen, The analytic variation of p-adic Hodge structure. Annals of Math.127 (1988) 647-661. Zbl0662.12018MR942523
  18. [Sh] G. Shimura, Introduction to the arithmetic theory of automorphic forms. Publ. Math. Soc. Japan II Tokyo Princeton (1971). Zbl0221.10029MR314766
  19. [Sw-D] P. Swinnerton-Dyer, On l-adic representations and congruences for coefficients of modular forms. Lecture Notes in Mathematics350 pp.1-55. Springer-Verlag, Berlin-Heidleberg- New York (1973). Zbl0267.10032MR406931
  20. [T] J. Tilouine, Un sous-groupe p-divisible de la jacobienne de X1(Nrp) comme module sur l'algèbre de Hecke. Bull. Math. Soc. Fr.115 (1987) 329-360. Zbl0677.14006MR926532

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