Sur la constante de Hida des courbes modulaires et des courbes de Shimura
Journal de Théorie des Nombres de Bordeaux, Volume 13 (2001) no. 1, pp. 325-337.

We compare the “modules of congruences between modular forms” of quotients of the new part of the jacobian J 0 (N) of X 0 (N) and quotients of the new part of the jacobian of some Shimura curves which are associated in the correspondance of Shimizu and Jacquet-Langlands.

La correspondance de Shimizu et Jacquet-Langlands donne des relations entre les quotients de la partie nouvelle de la jacobienne J 0 (N) de X 0 (N) et ceux de la partie nouvelle de la jacobienne de certaines courbes de Shimura associées. Nous comparons dans ce texte les congruences entre formes modulaires pour des quotients qui sont associés dans cette correspondance.

@article{JTNB_2001__13_1_325_0,
     author = {Emmanuel Ullmo},
     title = {Sur la constante de {Hida} des courbes modulaires et des courbes de {Shimura}},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {325--337},
     publisher = {Universit\'e Bordeaux I},
     volume = {13},
     number = {1},
     year = {2001},
     doi = {10.5802/jtnb.325},
     zbl = {1047.11059},
     mrnumber = {1838091},
     language = {fr},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.325/}
}
TY  - JOUR
TI  - Sur la constante de Hida des courbes modulaires et des courbes de Shimura
JO  - Journal de Théorie des Nombres de Bordeaux
PY  - 2001
DA  - 2001///
SP  - 325
EP  - 337
VL  - 13
IS  - 1
PB  - Université Bordeaux I
UR  - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.325/
UR  - https://zbmath.org/?q=an%3A1047.11059
UR  - https://www.ams.org/mathscinet-getitem?mr=1838091
UR  - https://doi.org/10.5802/jtnb.325
DO  - 10.5802/jtnb.325
LA  - fr
ID  - JTNB_2001__13_1_325_0
ER  - 
%0 Journal Article
%T Sur la constante de Hida des courbes modulaires et des courbes de Shimura
%J Journal de Théorie des Nombres de Bordeaux
%D 2001
%P 325-337
%V 13
%N 1
%I Université Bordeaux I
%U https://doi.org/10.5802/jtnb.325
%R 10.5802/jtnb.325
%G fr
%F JTNB_2001__13_1_325_0
Emmanuel Ullmo. Sur la constante de Hida des courbes modulaires et des courbes de Shimura. Journal de Théorie des Nombres de Bordeaux, Volume 13 (2001) no. 1, pp. 325-337. doi : 10.5802/jtnb.325. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.325/

[1] S. Bosch, W. Lutkebohmert, M. Raynaud, Néron models. Springer-Verlag New York, 1990. | MR: 1045822 | Zbl: 0705.14001

[2] M. Bertolini, H. Darmon, Heegner points on Mumford-Tate curves. Invent. Math 126 (1996),no. 3, 413-456. | MR: 1419003 | Zbl: 0882.11034

[3] K. Buzzard, Integral models of certain Shimura curves. Duke. Math. Journ. 87 (1997), 591-612. | MR: 1446619 | Zbl: 0880.11048

[4] B. Gross, Heights and the Special values of L-series. Canadian Math. Soc. Conf. Proc. 7 (1997), 115-187. | MR: 894322 | Zbl: 0623.10019

[5] A. Grothendieck, Groupe de Monodromie en Géométrie Algébrique. SGA 7 I, Lecture notes in Math. 288, Springer Verlag, 1972. | Zbl: 0237.00013

[6] B. Jordan, R. Livne, On the Néron Model of Jacobian of Shimura Curves. Compositio Math. 60 (1986), 227-236 | Numdam | MR: 868139 | Zbl: 0609.14018

[7] H. Hida, Congruences for cusps forms and special values of their zeta functions. Invent. Math 63 (1981), 225-261. | MR: 610538 | Zbl: 0459.10018

[8] H. Hida, On congruence divisors of cusp forms as factors of the special values of their zeta functions. Invent. Math 64 (1981), 225-261. | MR: 629471 | Zbl: 0472.10028

[9] B. Mazur, Modular Curves and the Eisenstein Ideal. Pub. Math. IHES 47 (1977), 33-186. | Numdam | MR: 488287 | Zbl: 0394.14008

[10] B. Mazur, Rational isogenies of prime degree. Invent. Math 44 (1978), 129-162. | MR: 482230 | Zbl: 0386.14009

[11] M. Raynaud, Hauteurs et isogénies. Astérisque 127 (1985), 199-234. | MR: 801923

[12] M. Raynaud, Jacobienne des courbes modulaires. Astérisque 196-197 (1991), 9-25. | MR: 1141454 | Zbl: 0781.14020

[13] K. Ribet, On modular representations of rm Gal(Q/Q) arising from modular forms. Invent. Math. 100 (1990), 431-471. | MR: 1047143 | Zbl: 0773.11039

[14] K. Ribet, Congruence relation between modular forms. Proc. Int. Congr. Math. (1983), 503-514. | MR: 804706 | Zbl: 0575.10024

[15] K. Ribet, Mod p Hecke operators and congruences between modular forms. Invent. Math. (1983), 193-205. | MR: 688264 | Zbl: 0508.10018

[16] K. Ribet, S. Takahashi, Parametrisation of elliptic curves by Shimura curves and by classical modular curves. Proc. Natl. Acad. Sci. USA 94 (1997), 11110-11114. | MR: 1491967 | Zbl: 0897.11018

[17] E. Ullmo, Hauteur de Faltings de quotients de J0(N), discriminants d'algèbres de Hecke et congruences entre formes modulaires. Amer. J. of Math. 122 (2000), 83-115. | MR: 1737258 | Zbl: 0991.11033

[18] M.-F. Vignéras, Arithmétique des algèbres de quaternions. Lect. Notes. Maths 800, Springer-Verlag New-York, 1980. | MR: 580949 | Zbl: 0422.12008

Cited by Sources: