Iwasawa modules attached to congruences of cusp forms

Haruzo Hida

Annales scientifiques de l'École Normale Supérieure (1986)

  • Volume: 19, Issue: 2, page 231-273
  • ISSN: 0012-9593

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Hida, Haruzo. "Iwasawa modules attached to congruences of cusp forms." Annales scientifiques de l'École Normale Supérieure 19.2 (1986): 231-273. <http://eudml.org/doc/82176>.

@article{Hida1986,
author = {Hida, Haruzo},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {congruences; cusp forms; -adic modular forms; Hecke algebra; Iwasawa algebra},
language = {eng},
number = {2},
pages = {231-273},
publisher = {Elsevier},
title = {Iwasawa modules attached to congruences of cusp forms},
url = {http://eudml.org/doc/82176},
volume = {19},
year = {1986},
}

TY - JOUR
AU - Hida, Haruzo
TI - Iwasawa modules attached to congruences of cusp forms
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1986
PB - Elsevier
VL - 19
IS - 2
SP - 231
EP - 273
LA - eng
KW - congruences; cusp forms; -adic modular forms; Hecke algebra; Iwasawa algebra
UR - http://eudml.org/doc/82176
ER -

References

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  1. [1] N. BOURBAKI, Commutative algebra, Hermann, Paris, 1972. MR360549
  2. [2] L. CARLITZ, Arithmetic properties of generalized Bernoulli numbers (J. reine angew. Math., Vol. 202, 1959, pp. 174-182). Zbl0125.02202MR109132
  3. [3] P. DELIGNE and M. RAPOPORT, Les schémas de modules des courbes elliptiques, in : Modular functions of one variable, II (Lecture notes in Math., Vol. 349, pp. 143-174, Springer, 1973). Zbl0281.14010MR337993
  4. [4] K. DOI and T. MIYAKE, Automorphic forms and number theory (in Japanese), Kinokuniya Shoten, Tokyo, 1976. Zbl0466.10012
  5. [5] E. HECKE, Zur Theorie der elliptischen module Funktionen (Math. Ann., Vol. 97, 1926, pp. 210-242 (= Werke No. 23)). Zbl52.0377.04JFM52.0377.04
  6. [6] E. HECKE, Theorie der Eisensteinschen Reihen höherer Stufe und ihre Anwendung auf Funktionentheorie und Arithmetik (Abh. Math. Sem. Hamburg, Vol. 5, 1927, pp. 199-224 (= Werke No. 24)). Zbl53.0345.02JFM53.0345.02
  7. [7] H. HIDA, Congruences of cusp forms and special values of their zeta functions (Inventiones Math., Vol. 63, 1981, pp. 225-261). Zbl0459.10018MR610538
  8. [8] H. HIDA, On congruence divisors of cusp forms as factors of the special values of their zeta functions (Inventiones Math., Vol. 64, 1981, pp. 221-262). Zbl0472.10028MR629471
  9. [9] H. HIDA, Kummer's criterion for the special values of Hecke L-functions of imaginary quadratic fields and congruences among cusp forms (Inventiones Math., Vol. 66, 1982, pp. 415-459). Zbl0485.10019MR662601
  10. [10] H. HIDA, A p-adic measure attached to the zeta functions associated with two elliptic modular forms, I (Inventiones Math., Vol. 79, 1985, pp. 159-195). Zbl0573.10020MR774534
  11. [11] H. HIDA, Galois representations into GL2 (Zp[[X]]) attached to ordinary cusp forms, to appear in Inventiones Math. Zbl0612.10021MR848685
  12. [12] K. IWASAWA, On Γ-extensions of algebraic number fields, Bull. (Amer. Math. Soc., Vol. 65, 1959, pp. 183-226). Zbl0089.02402MR124316
  13. [13] N. JOCHNOWITZ, Congruences between systems of eigenvalues of modular forms (Trans. Amer. Math. Soc., Vol. 270, 1982, pp. 269-285). Zbl0536.10022MR642341
  14. [14] N. M. KATZ, p-adic properties of modular schemes and modular forms, in : Modular functions of one variable, III (Lecture notes in Math., Vol. 350, 1973, pp. 69-190). Zbl0271.10033MR447119
  15. [15] N. M. KATZ, p-adic L-functions via moduli of elliptic curves (Proc. Symp. Pure Math., Vol. 29, 1975, pp. 479-506). Zbl0317.14009MR432649
  16. [16] N. M. KATZ, Higher congruences between modular forms (Ann. of Math., Vol. 101, 1975, pp. 332-367). Zbl0356.10020MR417059
  17. [17] N. M. KATZ, The Eisenstein measure and p-adic interpolation (Amer. J. Math., Vol. 99, 1977, pp. 238-311). Zbl0375.12022MR485797
  18. [18] N. M. KATZ, p-adic interpolation of real analytic Eisenstein series (Ann. of Math., Vol. 104, 1976, pp. 459-571). Zbl0354.14007MR506271
  19. [19] S. LANG, Introduction to modular forms, Grundlehren der Math. Wiss., Vol. 222, Springer, 1976. Zbl0344.10011MR429740
  20. [20] S. LANG, Cyclotomic fields, Grad. Texts in Math., Vol. 59, Springer, 1978. Zbl0395.12005MR485768
  21. [21] K. MAHLER, p-adic numbers and their functions, Cambridge Univ. Press, Cambridge, 1981. Zbl0444.12013MR644483
  22. [22] B. MAZUR, Modular curves and the Eisenstein ideal (Publ. Math. I.H.E.S., Vol. 47, 1977, pp. 33-186). Zbl0394.14008MR488287
  23. [23] T. MIYAKE, On automorphic forms on GL2 and Hecke operators (Ann. of Math., Vol. 94, 1971, pp. 174-189). Zbl0204.54201MR299559
  24. [24] K. A. RIBET, Mod p Hecke operators and congruences between modular forms (Inventiones Math., Vol. 71, 1983, p. 193-205). Zbl0508.10018MR688264
  25. [25] J.-P. SERRE, Classes des corps cyclotomiques, d'après Iwasawa, Séminaire Bourbaki, 1958. Zbl0119.27603
  26. [26] G. SHIMURA, On elliptic curves with complex multiplication as factors of the jacobians of modular function fields (Nagoya Math. J., Vol. 43, 1971, pp. 199-208). Zbl0225.14015MR296050
  27. [27] G. SHIMURA, On the Fourier coefficients of modular forms of several variables (Göttingen Nachr. Akad. Wiss., 1975, pp. 261-268). Zbl0332.32024MR485706
  28. [28] G. SHIMURA, The periods of certain automorphic forms of arithmetic type (J. Fac. Sci. Univ. Tokyo, Sec. IA, Vol. 28, 1982, pp. 605-632). Zbl0499.10027MR656039
  29. [29] G. SHIMURA, Introduction to the arithmetic theory of automorphic functions, Iwanami Shoten and Princeton Univ. Press, 1971. Zbl0221.10029
  30. [30] A. WEIL, L'intégration dans les groupes topologiques et ses applications, Hermann, Paris, 1958. 
  31. [31] H. HIDA, Congruences of cusp forms and Hecke algebras, Séminaire de Théorie des Nombres, Paris, 1983-1984, Progress in Math. No 59, pp. 133-146. Zbl0575.10025MR902830

Citations in EuDML Documents

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  1. Vincent Pilloni, Overconvergent modular forms
  2. Ami Fischman, On the image of Λ -adic Galois representations
  3. Vincent Pilloni, Sur la théorie de Hida pour le groupe GSp 2 g
  4. Jacques Tilouine, Théorie d'Iwasawa de l'algèbre de Hecke ordinaire et théorie d'Iwasawa classique
  5. Eknath Ghate, Vinayak Vatsal, On the local behaviour of ordinary Λ -adic representations
  6. B. Mazur, Two-dimensional p -adic Galois representations unramified away from p
  7. Robert F. Coleman, Classical and overconvergent modular forms
  8. Fred Diamond, On congruence modules associated to Λ -adic forms
  9. Masami Ohta, Congruence modules related to Eisenstein series
  10. Trevor Arnold, Hida families, p -adic heights, and derivatives

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