On the search of genuine p-adic modular L-functions for GL(n). With a correction to : on p-adic L-functions of GL(2)×GL(2) over totally real fields
Mémoires de la Société Mathématique de France, no. 67 (1996) , 116 p.
@book{MSMF_1996_2_67__R1_0,
     author = {Hida, Haruzo},
     title = {On the search of genuine $p$-adic modular $L$-functions for $GL(n)$. {With} a correction to : on $p$-adic $L$-functions of $GL(2)\times {}GL(2)$ over totally real fields},
     series = {M\'emoires de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {67},
     year = {1996},
     doi = {10.24033/msmf.381},
     zbl = {0897.11015},
     language = {en},
     url = {http://archive.numdam.org/item/MSMF_1996_2_67__R1_0/}
}
TY  - BOOK
AU  - Hida, Haruzo
TI  - On the search of genuine $p$-adic modular $L$-functions for $GL(n)$. With a correction to : on $p$-adic $L$-functions of $GL(2)\times {}GL(2)$ over totally real fields
T3  - Mémoires de la Société Mathématique de France
PY  - 1996
DA  - 1996///
IS  - 67
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/MSMF_1996_2_67__R1_0/
UR  - https://zbmath.org/?q=an%3A0897.11015
UR  - https://doi.org/10.24033/msmf.381
DO  - 10.24033/msmf.381
LA  - en
ID  - MSMF_1996_2_67__R1_0
ER  - 
%0 Book
%A Hida, Haruzo
%T On the search of genuine $p$-adic modular $L$-functions for $GL(n)$. With a correction to : on $p$-adic $L$-functions of $GL(2)\times {}GL(2)$ over totally real fields
%S Mémoires de la Société Mathématique de France
%D 1996
%N 67
%I Société mathématique de France
%U https://doi.org/10.24033/msmf.381
%R 10.24033/msmf.381
%G en
%F MSMF_1996_2_67__R1_0
Hida, Haruzo. On the search of genuine $p$-adic modular $L$-functions for $GL(n)$. With a correction to : on $p$-adic $L$-functions of $GL(2)\times {}GL(2)$ over totally real fields. Mémoires de la Société Mathématique de France, Serie 2, , no. 67 (1996), 116 p. doi : 10.24033/msmf.381. http://numdam.org/item/MSMF_1996_2_67__R1_0/

[1] Y. André, p-adic Betti lattices, In &201C;p-adic Analysis&201D;, Lecture notes in Math. 1454 (1989), 23-63. | MR | Zbl

[2] D. Blasius, A p-adic property of Hodge classes of abelian varieties, Proc. Symp. Pure Math. 55 Part 2 (1994), 293-308. | MR | Zbl

[3] D. Blasius, Period relations and critical values of L-functions, preprint, 1989.

[4] D. Blasius, On the critical values of Hecke L-series, Ann. of Math. 124 (1986), 23-63. | MR | Zbl

[5] D. Blasius, Appendix to Orloff Critical values of certain tensor product L-functions, Invent. Math. 90 (1987), 181-188. | MR | Zbl

[6] D. Blasius and J. D. Rogawski, Motives for Hilbert modular forms, Inventiones Math. 114 (1993), 55-87. | MR | Zbl

[7] S. Bloch and K. Kato, L-functions and Tamagawa numbers of motives, Progress in Math. (Grothendieck Festschrift 1) 86 (1990), 333-400. | MR | Zbl

[8] N. Bourbaki, Algèbre commutative, Hermann Paris, 1961-1965.

[9] H. Carayol, Sur les représentations l-adiques associées aux formes modulaires de Hilbert, Ann. Sci. Éc. Norm. Sup. 4-th series, 19 (1986), 409-468. | Numdam | MR | Zbl

[10] H. Carayol, Formes modulaires et représentations galoisiennes à valeurs dans un anneau local compact, Contemporary Math. 165 (1994), 213-237. | MR | Zbl

[11] W. Casselman, On some results of Atkin and Lehner, Math. Ann. 201 (1973), 301-314. | MR | Zbl

[12] P. Colmez, Résidu en s = 1 des fonctions zêta p-adiques, Inventiones Math. 91 (1988), 371-389. | MR | Zbl

[13] P. Colmez, Fonctions zêta p-adiques en s = 0, J. reine angew. Math. 467 (1995), 89-107. | MR | Zbl

[14] P. Colmez and L. Schneps, p-adic interpolation of special values of Hecke L-functions, Compositio Math. 82 (1992), 143-187. | Numdam | MR | Zbl

[15] P. Deligne, Valeurs des fonctions L et périodes d'intégrales, Proc. Symp. Pure Math. 33 (1979), part 2, 313-346. | MR | Zbl

[16] P. Deligne, Hodge cycles on abelian varieties, Lecture Notes in Math. 900 (1982), 9-100. | MR | Zbl

[17] P. Deligne and K. A. Ribet, Values of abelian L-functions at negative integers over totally real fields, Invent. Math. 59 (1980), 227-286. | MR | Zbl

[18] P. Deligne and J.S. Milne, Tannakian categories, Lecture notes in Math. 900 (1982), 101-228. | MR | Zbl

[19] K. Doi, H. Hida and H. Ishii, Discriminant of Hecke fields and the twisted adjoint L-values for GL(2), preprint, 1996.

[20] G. Faltings, Crystalline cohomology and p-adic Galois representations, Proc. JAMI inaugural Conference, supplement to Amer. J. Math. (1988), 25-80. | MR | Zbl

[21] G. Faltings, p-adic Hodge theory, J. Amer. Math. Soc. 1 (1988), 255-299. | MR | Zbl

[22] J.-M. Fontaine, Sur certains types de représentations p-adiques du group de Galois d'un corps local; construction d'un anneau de Barsotti-Tate, Ann. of Math. 115 (1982), 529-577. | MR | Zbl

[23] J.-M. Fontaine, Modules galoisiens, modules filtrés et anneaux de Barsotti-Tate, Astérisque 65 (1979), 3-80. | MR | Zbl

[24] J.-M. Fontaine and W. Messing, p-adic periods and p-adic étale cohomology, Contemporary Math. 67 (1987), 179-207. | MR | Zbl

[25] K. Fujiwara, Deformation rings and Hecke algebras in totally real case, preprint, 1996.

[26] S. Gelbart and H. Jacquet, A relation between automorphic representations of GL(2) and GL(3), Ann. Scient. Ec. Norm. Sup. 4-th series 11 (1978), 471-542. | Numdam | MR | Zbl

[27] R. Gillard, Relations monomiales entre périodes p-adiques, Invent. Math. 93 (1988), 355-381. | MR | Zbl

[28] R. Greenberg, Iwasawa theory and p-adic deformations of motives, Proc. Symp. Pure Math. 55 (1994) Part 2, 193-223. | MR | Zbl

[29] R. Greenberg, Iwasawa theory for p-adic representations, Adv. Studies Pure Math. 17 (1989), 97-137. | MR | Zbl

[30] M. Harris, Period invariants of Hilbert modular forms I: Trilinear differential operators and L-functions, Lecture note in Math. 1447 (1990), 155-202. | MR | Zbl

[31] M. Harris, L-functions of 2×2 unitary groups and factorization of periods of Hilbert modular forms, J. Amer. Math. Soc. 6 (1993), 637-719. | MR | Zbl

[32] M. Harris and J. Tilouine, p-adic measures and square roots of triple product L-functions, preprint, 1994.

[33] H. Hida, Elementary Theory of L-functions and Eisenstein series, LMSST 26, Cambridge University Press, 1993. | MR | Zbl

[34] H. Hida, On p-adic Hecke algebras for GL2 over totally real fields, Ann. of Math. 128 (1988), 295-384. | MR | Zbl

[35] H. Hida, On nearly ordinary Hecke algebras for GL(2) over totally real fields, Adv. Studies in Pure Math. 17 (1989), 139-169. | MR | Zbl

[36] H. Hida, Iwasawa modules attached to congruences of cusp forms, Ann. Sci. Ec. Norm. Sup. 4-ème série 19 (1986), 231-273. | Numdam | MR | Zbl

[37] H. Hida, A p-adic measure attached to the zeta functions associated with two elliptic modular forms I, Inventiones Math. 79 (1985), 159-195; II, Ann. l'Institut Fourier 38 (1988), 1-83. | Numdam | Zbl

[38] H. Hida, Nearly ordinary Hecke algebras and Galois representations of several variables, Proc. JAMI inaugural Conference, supplement to Amer. J. Math. (1988), 115-134. | MR | Zbl

[39] H. Hida, Modules of congruence of Hecke algebras and L-functions associated with cusp forms, Amer. J. Math. 110 (1988), 323-382. | MR | Zbl

[40] H. Hida, Le produit de Petersson et de Rankin p-adique, Sém. Théorie des Nombres, 1988-1989, 87-102. | MR | Zbl

[41] H. Hida, On p-adic L-functions of GL(2) × GL(2) over totally real fields, Ann. l'Institut Fourier 41 No.2 (1991), 311-391. | Numdam | MR | Zbl

[42] H. Hida, On the critical values of L-functions of GL(2) and GL(2) × GL(2), Duke Math. J. 74 (1994), 431-529. | MR | Zbl

[43] H. Hida, Congruences of cusp forms and special values of their zeta functions, Inventiones Math. 63 (1981), 225-261. | MR | Zbl

[44] H. Hida, Galois representations into GL2 (ℤp[[X]]) attached to ordinary cusp forms, Inventiones Math. 85 (1986), 545-613. | MR | Zbl

[45] H. Hida, On Selmer groups of adjoint modular Galois representations, Number Theory, Paris, LMS lecture notes series, 1996. | MR | Zbl

[46] H. Hida, Non-critical values of adjoint L-functions for SL(2), preprint, 1997.

[47] H. Hida and J. Tilouine, Anti-cyclotomic Katz p-adic L-functions and congruence modules, Ann. Scient. Ec. Norm. Sup. 26 (1993), 189-259. | Numdam | MR | Zbl

[48] H. Hida and J. Tilouine, On the anticyclotomic main conjecture for CM fields, Inventiones Math. 117 (1994), 89-147. | MR | Zbl

[49] H. Hida, J. Tilouine, and E. Urban, Adjoint modular Galois representations and their Selmer groups, Proc. NAS. 1997 | MR | Zbl

[50] Luc Illusie, Cohomologie de de Rham et cohomologie étale p-adique, Séminaire Bourbaki, 1989-1990 no. 726 | Numdam | Zbl

[51] H. Jacquet, Automorphic forms on GL(2), II, Lecture notes in Math. 278, Springer, 1972 | MR | Zbl

[52] N. M. Katz, p-adic L-functions for CM fields, Inventiones Math. 49 (1978), 199-297 | MR | Zbl

[53] K. Kitagawa, On standard p-adic L-functions of families of elliptic cusp forms, Contemporary Math. 165 (1994), 81-110 | MR | Zbl

[54] B. Mazur, Deforming Galois representations, in "Galois group over ℚ", MSRI publications 16, (1989), 385-437 | MR | Zbl

[55] B. Mazur and J. Tilouine, Représentations Galoisiennes, différentielles de Kähler et "conjectures principales", Publ. IHES 71 (1990), 65-103 | Numdam | MR | Zbl

[56] A. A. Panchishkin, Admissible non-archimedean standard zeta functions associated with Siegel modular forms, Proc. Symp. Pure Math. 55 Part 2 (1994), 251-292 | MR | Zbl

[57] A. A. Panchishkin, Produits triples des formes modulaires et leur interpolation p-adique par la méthode d'Amice-Vélu, preprint 1993

[58] B. Perrin-Riou, Fonction L p-adiques des représentations p-adiques, Astérisque 229 (1995) | Zbl

[59] B. Perrin-Riou, Variation de la fonction L p-adique par isogénie, Adv. Studies Pure Math. 17 (1989), 347-358 | MR | Zbl

[60] B. Perrin-Riou, Représentations p-adiques, périodes et fonctions L p-adiques, Séminaire de théorie des nombres, Paris (1987-1988), 213-258 | MR | Zbl

[61] J.-P. Serre, Abelian l-adic representations and elliptic curves, Benjamin, 1968 | MR | Zbl

[62] J.-P. Serre, Groupes algébriques associés aux modules de Hodge-Tate, Astérisque 65 (1979), 155-188 | MR | Zbl

[63] J.-P. Serre, Propriétés conjecturales des groupes de Galois motiviques et des représentations l-adiques, Proc. Symp. Pure Math. 55, Part 1, 377-400 | MR | Zbl

[64] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Iwanami-Shoten and Princeton Univ. Press, 1971 | Zbl

[65] G. Shimura, The special values of the zeta functions associated with Hilbert modular forms, Duke Math. J. 45 (1978), 637-679 | MR | Zbl

[66] G. Shimura, On the critical values of certain Dirichlet series and the periods of automorphic forms, Inventiones Math. 94 (1988), 245-305 | MR | Zbl

[67] G. Shimura, On the fundamental periods of automorphic forms of arithmetic type, Inventiones Math. 102 (1990), 399-428 | MR | Zbl

[68] J. Tate, p-Divisible groups, Proc. of Conference on local fields, Driebergen 1966, 158-183 | MR | Zbl

[69] R. Taylor, On Galois representations associated to Hilbert modular forms, Inventiones Math. 98 (1989), 265-280 | MR | Zbl

[70] R. Taylor and A. Wiles, Ring theoretic properties of certain Hecke modules, Ann. of Math. 142 (1995), 553-572 | MR | Zbl

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

[72] J. Tilouine, Deformation of Galois representations and Hecke algebras, Publ. Mehta Res. Inst., Narosa Publ., Delhi, 1996 | Zbl

[73] A. Wiles, Modular elliptic curves and Fermat's last theorem, Ann. of Math. 142 (1995), 443-551 | MR | Zbl

[74] H. Yoshida, On the zeta functions of Shimura varieties and periods of Hilbert modular forms, Duke Math. J. 75 (1994), 121-191 | MR | Zbl

[75] H. Yoshida, On a conjecture of Shimura concerning periods of Hilbert modular forms, Amer. J. Math. 117 (1995), 1019-1038 | MR | Zbl

Cited by Sources: