Anti-cyclotomic Katz p -adic L -functions and congruence modules

H. Hida; J. Tilouine

Annales scientifiques de l'École Normale Supérieure (1993)

  • Volume: 26, Issue: 2, page 189-259
  • ISSN: 0012-9593

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Hida, H., and Tilouine, J.. "Anti-cyclotomic Katz $p$-adic $L$-functions and congruence modules." Annales scientifiques de l'École Normale Supérieure 26.2 (1993): 189-259. <http://eudml.org/doc/82340>.

@article{Hida1993,
author = {Hida, H., Tilouine, J.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {congruence modules; Katz -adic -functions; -adic theta series; interpolation; -adic Rankin product; -adic Eisenstein measures; -adic Hecke algebra; anti-cyclotomic main conjecture for CM-fields; divisibility of characteristic power series of congruence module; Iwasawa main conjecture for CM-fields},
language = {eng},
number = {2},
pages = {189-259},
publisher = {Elsevier},
title = {Anti-cyclotomic Katz $p$-adic $L$-functions and congruence modules},
url = {http://eudml.org/doc/82340},
volume = {26},
year = {1993},
}

TY - JOUR
AU - Hida, H.
AU - Tilouine, J.
TI - Anti-cyclotomic Katz $p$-adic $L$-functions and congruence modules
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1993
PB - Elsevier
VL - 26
IS - 2
SP - 189
EP - 259
LA - eng
KW - congruence modules; Katz -adic -functions; -adic theta series; interpolation; -adic Rankin product; -adic Eisenstein measures; -adic Hecke algebra; anti-cyclotomic main conjecture for CM-fields; divisibility of characteristic power series of congruence module; Iwasawa main conjecture for CM-fields
UR - http://eudml.org/doc/82340
ER -

References

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  1. [D1] P. DELIGNE, Equations différentielles à points singuliers réguliers (Lec. Notes in Math., No. 163, Springer, 1970). Zbl0244.14004MR54 #5232
  2. [DH] K. DOI and H. HIDA, On a Certain Congruence of Cusp Forms and the Special Values of their Dirichlet Series, unpublished, 1979. 
  3. [DR] P. DELIGNE and K. A. RIBET, Values of Abelian L-functions at Negative Integers Over Totally Real Field (Invent. Math., Vol. 59, 1980, pp. 227-286). Zbl0434.12009MR81m:12019
  4. [G] P. B. GARRETT, Holomorphic Hilbert Modular Forms, Wadsworth & Brooks/Cole, 1990. Zbl0685.10021MR90k:11058
  5. [GJ] S. GELBART and H. JACQUET, A Relation Between Automorphic Representations of GL(2) and GL(3) (Ann. Scient. Éc. Norm. Sup., 4e série, T. 11, 1978, pp. 471-542). Zbl0406.10022MR81e:10025
  6. [H1] H. HIDA, On p-adic L-functions of GL(2) × GL(2) Over Totally Real Fields (Ann. Institut Fourier, Vol. 41, 1991, pp. 311-391). Zbl0725.11025MR93b:11052
  7. [H2] H. HIDA, On p-adic Hecke Algebras for GL2 Over Totally Real Fields (Ann. of Math., Vol. 128, 1988, pp. 295-384). Zbl0658.10034MR89m:11046
  8. [H3] H. HIDA, On Nearly Ordinary Hecke Algebras for GL(2) Over Totally Real Fields (Advanced Study in Pure Math., Vol. 17, 1989, pp. 139-169). Zbl0742.11026MR92f:11064
  9. [H4] H. HIDA, Congruences of Cusp Forms and Special Values of their Zeta Functions (Inventiones Math., Vol. 63, 1981, pp. 225-261). Zbl0459.10018MR82g:10044
  10. [H5] H. HIDA, p-adic L-Functions for Base Change Lifts of GL2 to GL3, to appear in Proc. Ann Arbor Conference on Automorphic forms, Shimura Varieties, and L-functions, 1988, vol. II, pp. 93-142, Perspectives in Math., 11, 1990. Zbl0705.11033
  11. [H6] H. HIDA, Modules of Congruence of Hecke Algebras and L-functions Associated with Cusp Forms (Amer. J. Math., Vol. 110, 1988, pp. 323-382). Zbl0645.10029MR89i:11058
  12. [HT1] H. HIDA and J. TILOUINE, Katz p-adic L-functions, Congruence Modules and Deformation of Galois Representations (Proceedings of Durham Symposium on Arithmetic of L-functions, 1989). Zbl0739.11022
  13. [HT2] H. HIDA and J. TILOUINE, On the Anti-cyclotomic Main Conjecture for CM Fields, preprint. Zbl0819.11047
  14. [K1] N. M. KATZ, Travaux de Dwork (Séminaire Bourbaki, 409, 1972). 
  15. [K2] N. M. KATZ, Nilpotent Connections and the Monodromy Theorem. Applications of a Result of Turrittin (Publ. Math. I.H.E.S., Vol. 39, 1970, pp. 175-232). Zbl0221.14007MR45 #271
  16. [K3] N. M. KATZ, Serre-Tate Local Moduli, in Surfaces algébriques (Lecture Notes in Math., No. 868, Springer, 1978, pp. 138-202. Zbl0477.14007MR83k:14039b
  17. [K4] N. M. KATZ, p-adic L-functions for CM Fields (Invent. Math., Vol. 49, 1878, pp. 199-297). Zbl0417.12003MR80h:10039
  18. [KO] N. M. KATZ, and T. ODA, On the Differentiation of the De Rham Cohomology Classes with Respect to Parameters (J. Math. Kyoto Univ., Vol. 8, 1968, pp. 199-213). Zbl0165.54802MR38 #5792
  19. [Kn] D. KNUTSON, Algebraic Spaces (Springer Lecture Notes in Math., No. 203). Zbl0221.14001MR46 #1791
  20. [M] D. MUMFORD, An Analytic Construction of Degenerating Abelian Varieties Over Complete Rings (Comp. Math., Vol. 24, 1972, pp. 239-272). Zbl0241.14020MR50 #4593
  21. [MT] B. MAZUR and J. TILOUINE, Représentations galoisiennes, différentielles de Kähler et conjectures principales (Publ. I.H.E.S., No. 71, 1990, pp. 65-103). Zbl0744.11053MR92e:11060
  22. [R] M. RAPOPORT, Compactifications de l'espace de modules de Hilbert-Blumenthal (Composition Math., Vol. 36, 1978, pp. 255-335). Zbl0386.14006MR80j:14009
  23. [Sch] C.-G. SCHMIDT, P-adic Measures Attached to Automorphic Representations of GL(3) [Inventiones Math., Vol. 92, 1988, pp. 597-631]. Zbl0656.10023MR90f:11032
  24. [Sh] G. SHIMURA, On Some Arithmetic Properties of Modular Forms of One and Several Variables (Ann. of Math., Vol. 102, 1975, pp. 491-515). Zbl0327.10028MR58 #10758
  25. [T] J. TILOUINE, Sur la conjecture principale anticyclotomique (Duke Math. J., Vol. 59, 1989, pp. 629-673). Zbl0707.11079MR91b:11118
  26. [W] A. WEIL, Basic Number Theory, Springer, 1974. Zbl0326.12001MR55 #302
  27. [Y] H. YOSHIDA, On the Representation of the Galois Groups Obtained from Hilbert Modular Forms (Thesis, Princeton University, 1973). 

Citations in EuDML Documents

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  1. Haruzo Hida, p -adic ordinary Hecke algebras for GL ( 2 )
  2. Thanasis Bouganis, Non-abelian p -adic L -functions and Eisenstein series of unitary groups – The CM method
  3. Mladen Dimitrov, Galois representations modulo p and cohomology of Hilbert modular varieties
  4. Haruzo Hida, On the search of genuine p -adic modular L -functions for G L ( n ) . With a correction to: On p -adic L -functions of G L ( 2 ) × G L ( 2 ) over totally real fields
  5. Pierre Colmez, La conjecture de Birch et Swinnerton-Dyer 𝐩 -adique

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