Anti-cyclotomic Katz p-adic L-functions and congruence modules
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 26 (1993) no. 2, pp. 189-259. 
@article{ASENS_1993_4_26_2_189_0,
     author = {Hida, H. and Tilouine, J.},
     title = {Anti-cyclotomic {Katz} $p$-adic $L$-functions and congruence modules},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {189--259},
     publisher = {Elsevier},
     volume = {Ser. 4, 26},
     number = {2},
     year = {1993},
     doi = {10.24033/asens.1671},
     zbl = {0778.11061},
     mrnumber = {1209708},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/asens.1671/}
}
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Hida, H.; Tilouine, J. Anti-cyclotomic Katz $p$-adic $L$-functions and congruence modules. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 26 (1993) no. 2, pp. 189-259. doi : 10.24033/asens.1671. https://www.numdam.org/articles/10.24033/asens.1671/

[D1] P. Deligne, Equations différentielles à points singuliers réguliers (Lec. Notes in Math., No. 163, Springer, 1970). | MR | Zbl

[DH] K. Doi and H. Hida, On a Certain Congruence of Cusp Forms and the Special Values of their Dirichlet Series, unpublished, 1979.

[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). | MR | Zbl

[G] P. B. Garrett, Holomorphic Hilbert Modular Forms, Wadsworth & Brooks/Cole, 1990. | MR | Zbl

[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). | Numdam | MR | Zbl

[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). | Numdam | MR | Zbl

[H2] H. Hida, On p-adic Hecke Algebras for GL2 Over Totally Real Fields (Ann. of Math., Vol. 128, 1988, pp. 295-384). | MR | Zbl

[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). | MR | Zbl

[H4] H. Hida, Congruences of Cusp Forms and Special Values of their Zeta Functions (Inventiones Math., Vol. 63, 1981, pp. 225-261). | MR | Zbl

[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. | Zbl

[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). | MR | Zbl

[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). | Zbl

[HT2] H. Hida and J. Tilouine, On the Anti-cyclotomic Main Conjecture for CM Fields, preprint.

[K1] N. M. Katz, Travaux de Dwork (Séminaire Bourbaki, 409, 1972). | Numdam

[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). | Numdam | MR | Zbl

[K3] N. M. Katz, Serre-Tate Local Moduli, in Surfaces algébriques (Lecture Notes in Math., No. 868, Springer, 1978, pp. 138-202. | MR | Zbl

[K4] N. M. Katz, p-adic L-functions for CM Fields (Invent. Math., Vol. 49, 1878, pp. 199-297). | MR | Zbl

[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). | MR | Zbl

[Kn] D. Knutson, Algebraic Spaces (Springer Lecture Notes in Math., No. 203). | MR | Zbl

[M] D. Mumford, An Analytic Construction of Degenerating Abelian Varieties Over Complete Rings (Comp. Math., Vol. 24, 1972, pp. 239-272). | Numdam | MR | Zbl

[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). | Numdam | MR | Zbl

[R] M. Rapoport, Compactifications de l'espace de modules de Hilbert-Blumenthal (Composition Math., Vol. 36, 1978, pp. 255-335). | Numdam | MR | Zbl

[Sch] C.-G. Schmidt, P-adic Measures Attached to Automorphic Representations of GL(3) [Inventiones Math., Vol. 92, 1988, pp. 597-631]. | MR | Zbl

[Sh] G. Shimura, On Some Arithmetic Properties of Modular Forms of One and Several Variables (Ann. of Math., Vol. 102, 1975, pp. 491-515). | MR | Zbl

[T] J. Tilouine, Sur la conjecture principale anticyclotomique (Duke Math. J., Vol. 59, 1989, pp. 629-673). | MR | Zbl

[W] A. Weil, Basic Number Theory, Springer, 1974. | MR | Zbl

[Y] H. Yoshida, On the Representation of the Galois Groups Obtained from Hilbert Modular Forms (Thesis, Princeton University, 1973).

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