@article{ASENS_2004_4_37_5_663_0,
author = {Diamond, Fred and Flach, Matthias and Guo, Li},
title = {The {Tamagawa} number conjecture of adjoint motives of modular forms},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {663--727},
year = {2004},
publisher = {Elsevier},
volume = {Ser. 4, 37},
number = {5},
doi = {10.1016/j.ansens.2004.09.001},
mrnumber = {2103471},
zbl = {02136287},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.ansens.2004.09.001/}
}
TY - JOUR AU - Diamond, Fred AU - Flach, Matthias AU - Guo, Li TI - The Tamagawa number conjecture of adjoint motives of modular forms JO - Annales scientifiques de l'École Normale Supérieure PY - 2004 SP - 663 EP - 727 VL - 37 IS - 5 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.ansens.2004.09.001/ DO - 10.1016/j.ansens.2004.09.001 LA - en ID - ASENS_2004_4_37_5_663_0 ER -
%0 Journal Article %A Diamond, Fred %A Flach, Matthias %A Guo, Li %T The Tamagawa number conjecture of adjoint motives of modular forms %J Annales scientifiques de l'École Normale Supérieure %D 2004 %P 663-727 %V 37 %N 5 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.ansens.2004.09.001/ %R 10.1016/j.ansens.2004.09.001 %G en %F ASENS_2004_4_37_5_663_0
Diamond, Fred; Flach, Matthias; Guo, Li. The Tamagawa number conjecture of adjoint motives of modular forms. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 5, pp. 663-727. doi: 10.1016/j.ansens.2004.09.001
[1] et al. , Séminaire de Géométrie Algébrique 1, Lecture Notes in Math., vol. 224, Springer-Verlag, 1971.
[2] et al. , Séminaire de Géométrie Algébrique 4, vol. 3, Lecture Notes in Math., vol. 305, Springer-Verlag, 1973. | MR
[3] , Représentations p-adiques et équations différentielles, Invent. Math. 148 (2) (2002) 219-284. | Zbl | MR
[4] , , L-functions and Tamagawa numbers of motives, in: The Grothendieck Festschrift, vol. 1, Birkhäuser, 1990, pp. 333-400. | Zbl | MR
[5] , , , , On the modularity of elliptic curves over : Wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001) 843-939. | Zbl | MR
[6] , Cohomology of Groups, Springer-Verlag, 1982. | Zbl | MR
[7] , , Tamagawa numbers for motives with (noncommutative) coefficients, Documenta Mathematica 6 (2001) 501-570. | Zbl | MR
[8] , , On the equivariant Tamagawa number conjecture for Tate motives, Invent. Math. 153 (2003) 303-359. | Zbl | MR
[9] , Sur les représentations ℓ-adiques attachées aux formes modulaires de Hilbert, C. R. Acad. Sci., Paris 296 (1983) 629-632. | Zbl | MR
[10] , , Iwasawa theory for the symmetric square of an elliptic curve, J. Reine Angew. Math. 375/376 (1987) 104-156. | Zbl | MR
[11] , , On the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 39 (1977) 223-251. | Zbl | MR
[12] , Théorie d'Iwasawa des représentations de de Rham d'un corps local, Ann. of Math. (2) 148 (2) (1998) 485-571. | Zbl | MR
[13] , , , Modularity of certain potentially Barsotti-Tate Galois representations, J. AMS 12 (1999) 521-567. | Zbl | MR
[14] , , , Fermat's Last Theorem, in: Current Development in Mathematics, International Press, 1995, pp. 1-154. | Zbl | MR
[15] , Formes modulaires et représentations ℓ-adiques, in: Séminaire Bourbaki 1968/1969, exposé 255, Lecture Notes in Math., vol. 179, 1969, pp. 139-172. | Zbl | Numdam
[16] , Les constantes de l'équation fonctionnelle des fonctions L, in: Modular Functions of One Variable. II, Lecture Notes in Math., vol. 349, Springer-Verlag, Berlin, 1997, pp. 501-595. | Zbl | MR
[17] , Valeurs de fonctions L et périodes d'intégrales, in: Automorphic Forms, Representations and L-functions, Proc. Symp. Pure Math., American Math. Soc., vol. 33, 1979, pp. 313-346. | Zbl | MR
[18] , , Les schémas de modules de courbes elliptiques, in: Lecture Notes in Math., vol. 349, 1973, pp. 143-316. | Zbl | MR
[19] , , Explicit construction of universal deformation rings, in: Elliptic Curves, Modular Forms and Fermat's Last Theorem, International Press, Cambridge, 1995, pp. 313-326. | Zbl | MR
[20] , Congruence primes for cusp forms of weight , Astérisque 196-197 (1991) 205-213. | Zbl | MR
[21] , The refined conjecture of Serre, in: Elliptic Curves, Modular Forms and Fermat's Last Theorem, International Press, Cambridge, 1995, pp. 22-37. | Zbl | MR
[22] , On deformation rings and Hecke rings, Annals of Math. 144 (1996) 137-166. | Zbl | MR
[23] , An extension of Wiles' results, in: Modular Forms and Fermat's Last Theorem, Springer-Verlag, 1997, pp. 475-489. | Zbl | MR
[24] , The Taylor-Wiles construction and multiplicity one, Invent. Math. 128 (1997) 379-391. | Zbl | MR
[25] Diamond, F., Flach, M., Guo, L., Adjoint motives of modular forms and the Tamagawa number conjecture, preprint.
[26] , , Non-optimal levels of mod ℓ modular representations, Invent. Math. 115 (1994) 435-462. | Zbl | MR
[27] , , Lifting modular mod ℓ representations, Duke Math. J. 74 (1994) 253-269. | Zbl | MR
[28] , On the modularity of certain 2-adic Galois representations, Duke Math. J. 109 (2001) 319-382. | Zbl | MR
[29] Dimitrov, M., Galois representations modulo p and cohomology of Hilbert modular varieties, Prépub. Math. de l'Univ. Paris 13, 2004-02. | MR
[30] , Serre's conjecture, in: Modular Forms and Fermat's Last Theorem, Springer-Verlag, 1997, pp. 209-242. | Zbl | MR
[31] , Crystalline cohomology and p-adic étale cohomology, in: Algebraic Analysis, Geometry and Number Theory, The John Hopkins University Press, 1989, pp. 25-80. | Zbl | MR
[32] Flach, M., Selmer groups for the symmetric square of an elliptic curve, thesis, Cambridge University, 1990.
[33] , A generalization of the Cassels-Tate pairing, J. Reine Angew. Math. 412 (1990) 113-127. | Zbl | MR
[34] , A finiteness theorem for the symmetric square of an elliptic curve, Invent. Math. 109 (1992) 307-327. | Zbl | MR
[35] , The equivariant Tamagawa number conjecture: a survey, in: , (Eds.), Proceedings of a Conference on Stark's Conjecture, Baltimore, 2002, Contemp. Math. Ser., AMS, 2004. | Zbl | MR
[36] , Modules galoisiens, modules filtrés et anneaux de Barsotti-Tate, in: Journées de Géométrie Algébrique de Rennes (III), Astérisque, vol. 65, Soc. Math. de France, 1979, pp. 3-80. | Zbl | MR | Numdam
[37] , Sur certains types de représentations p-adiques du groupe de Galois d'un corps local; Construction d'un anneau de Barsotti-Tate, Ann. Math. 115 (1982) 529-577. | Zbl | MR
[38] , Valeurs spéciales des fonctions L des motifs, in: Séminaire Bourbaki, exposé 751, février 1992, Astérisque, vol. 206, 1992, pp. 205-249. | Zbl | MR | Numdam
[39] , , Construction de représentations p-adiques, Ann. Sci. Éc. Norm. Sup. 15 (1982) 547-608. | Zbl | MR | Numdam
[40] , , Geometric Galois representations, in: Elliptic Curves, Modular Forms and Fermat's Last Theorem, International Press, 1995, pp. 41-78. | Zbl | MR
[41] , , Autour des conjectures de Bloch et Kato: cohomologie galoisienne et valeurs de fonction L, in: Motives, Proc. Symp. in Pure Math., vol. 55, 1994, pp. 599-706, Part 1. | Zbl | MR
[42] Fujiwara, K., Deformation rings and Hecke algebras in the totally real case, preprint. | MR
[43] , , A relation between automorphic representations of and , Ann. Sci. Éc. Norm. Sup., IV. Ser. 11 (1978) 471-542. | Zbl | MR | Numdam
[44] , Facteurs locaux des algèbres simples de rang 4. I, in: Groupes Réductifs et Formes Automorphes, I (Paris, 1976-77), Univ. Paris VII, 1978, pp. 37-77. | MR
[45] , , Heegner points and derivatives of L-series, Invent. Math. 84 (1986) 225-320. | Zbl | MR
[46] , , The Tame Fundamental Group of a Formal Neighbourhood of a Divisor with Normal Crossings on a Scheme, Springer-Verlag, 1971. | Zbl | MR
[47] , General Selmer groups and critical values of Hecke L-functions, Math. Ann. 297 (1993) 221-233. | Zbl | MR
[48] , On the Bloch-Kato conjecture for Hecke L-functions, J. Number Theory 57 (1996) 340-365. | Zbl | MR
[49] Harrison, M., On the conjecture of Bloch-Kato for Grössencharacters over , Ph.D. thesis, Cambridge University, 1993.
[50] , Algebraic Geometry, Springer-Verlag, Berlin, 1977. | Zbl | MR
[51] , Congruences of cusp forms and special values of their zeta functions, Invent. Math. 63 (1981) 225-261. | Zbl | MR
[52] , , Bloch-Kato conjecture and main conjecture of Iwasawa theory for Dirichlet characters, Duke Math. J. 119 (2003) 393-464. | Zbl | MR
[53] , Mixed Motives and Algebraic K-theory, Lect. Notes in Math., vol. 1400, Springer, 1990. | Zbl | MR
[54] , Logarithmic structures of Fontaine-Illusie, in: Algebraic Analysis, Geometry and Number Theory, The John Hopkins University Press, 1989, pp. 191-224. | Zbl | MR
[55] , Iwasawa theory and p-adic Hodge theory, Kodai Math. J. 16 (1993) 1-31. | Zbl | MR
[56] , Euler systems, Iwasawa theory and Selmer groups, Kodai Math. J. 22 (1999) 313-372. | Zbl | MR
[57] , The Tamagawa number conjecture for CM elliptic curves, Invent. Math. 143 (2001) 571-627. | Zbl | MR
[58] , The Mordell-Weil and Shafarevich-Tate groups for Weil elliptic curves, Izv. Akad. Nauk SSSR Ser. Mat. 52 (6) (1988) 1154-1180, 1327. Translation in, Math. USSR-Izv. 33 (3) (1989) 473-499. | Zbl | MR
[59] , , Finiteness of Ш over totally real fields, Izv. Akad. Nauk SSSR Ser. Mat. 55 (4) (1991) 851-876, Translation in, Math. USSR-Izv. 39 (1) (1992) 829-853. | Zbl
[60] , Complete intersections and Gorenstein rings, in: Elliptic Curves, Modular Forms and Fermat's Last Theorem, International Press, Cambridge, 1995. | Zbl | MR
[61] , An introduction to the deformation theory of Galois representations, in: Modular Forms and Fermat's Last Theorem, Springer-Verlag, 1997, pp. 243-311. | Zbl | MR
[62] , , Class fields of abelian extensions of , Invent. Math. 76 (1984) 179-330. | Zbl | MR
[63] , Modular Forms, Springer-Verlag, 1989. | Zbl | MR
[64] , On the p-adic height of Heegner cycles, Math. Ann. 302 (4) (1995) 609-686. | Zbl | MR
[65] , On a convolution of L-series, Invent. Math. 7 (1969) 297-312. | Zbl | MR
[66] , Théorie d'Iwasawa des représentations p-adiques sur un corps local, Invent. Math 115 (1994) 81-149. | Zbl | MR
[67] , Fonctions L p-adiques des représentations p-adiques, Astérisque 229 (1995). | Zbl | MR | Numdam
[68] , Congruence relations between modular forms, Proc. ICM 17 (1983) 503-514. | Zbl | MR
[69] , Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication, Invent. Math. 89 (1987) 527-560. | Zbl | MR
[70] , The “main conjecture” of Iwasawa theory for imaginary quadratic fields, Invent. Math. 103 (1991) 25-68. | Zbl
[71] , Modular forms and p-adic Hodge theory, Invent. Math. 129 (1997) 607-620. | Zbl | MR
[72] Savitt, D., Modularity of some potentially Barsotti-Tate Galois representations, Thesis, Harvard University, 2001.
[73] , p-adic measures attached to automorphic representations of , Invent. Math. 92 (1988) 597-631. | Zbl | MR
[74] , Modular forms and de Rham cohomology; Atkin-Swinnerton-Dyer congruences, Invent. Math. 79 (1985) 49-77. | Zbl | MR
[75] , Motives for modular forms, Invent. Math. 100 (1990) 419-430. | Zbl | MR
[76] , Géométrie algébrigue et géométrie analytique, Ann. Inst. Fourier 6 (1956) 1-42. | Zbl | MR | Numdam
[77] , Local Fields, Springer-Verlag, 1979. | Zbl | MR
[78] , Sur les représentations modulaires de degré 2 de , Duke Math. J. 54 (1987) 179-230. | Zbl | MR
[79] , Introduction to the Arithmetic Theory of Automorphic Functions, Iwanami Shoten and Princeton University Press, 1971. | Zbl | MR
[80] , On the holomorphy of certain Dirichlet series, Proc. London Math. Soc. 31 (1975) 79-98. | Zbl | MR
[81] , On the periods of modular forms, Math. Ann. 229 (1977) 211-221. | Zbl | MR
[82] , , Ordinary representations and modular forms, Proc. Nat. Acad. Sci. USA 94 (20) (1997) 10520-10527. | Zbl | MR
[83] , , Residually reducible representations and modular forms, IHÉS Publ. 89 (1999) 5-126, (2000). | Zbl | MR | Numdam
[84] , Special values of zeta functions and Eisenstein series of half integral weight, Amer. J. Math. 102 (1980) 219-240. | Zbl | MR
[85] , Evaluation of the symmetric square at the near center point, Amer. J. Math. 111 (1989) 585-598. | Zbl | MR
[86] , , Ring theoretic properties of certain Hecke algebras, Annals of Math. 141 (1995) 553-572. | Zbl | MR
[87] , p-adic étale cohomology and crystalline cohomology in the semi-stable reduction case, Invent. Math. 137 (2000) 233-411. | Zbl | MR
[88] , Modular elliptic curves and Fermat's Last Theorem, Annals of Math. 141 (1995) 443-551. | Zbl | MR
[89] , Heights of Heegner cycles and derivatives of L-series, Invent. Math. 130 (1997) 99-152. | Zbl | MR
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