@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}, volume = {37}, year = {2004}, pages = {663-727}, doi = {10.1016/j.ansens.2004.09.001}, mrnumber = {2103471}, zbl = {02136287}, language = {en}, url = {http://dml.mathdoc.fr/item/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, Tome 37 (2004) pp. 663-727. doi : 10.1016/j.ansens.2004.09.001. http://gdmltest.u-ga.fr/item/ASENS_2004_4_37_5_663_0/
[1] Séminaire de Géométrie Algébrique 1, Lecture Notes in Math., vol. 224, Springer-Verlag, 1971.
et al. ,[2] Séminaire de Géométrie Algébrique 4, vol. 3, Lecture Notes in Math., vol. 305, Springer-Verlag, 1973. | MR 354654
et al. ,[3] Représentations p-adiques et équations différentielles, Invent. Math. 148 (2) (2002) 219-284. | MR 1906150 | Zbl 01777245
,[4] L-functions and Tamagawa numbers of motives, in: The Grothendieck Festschrift, vol. 1, Birkhäuser, 1990, pp. 333-400. | MR 1086888 | Zbl 0768.14001
, ,[5] On the modularity of elliptic curves over : Wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001) 843-939. | MR 1839918 | Zbl 0982.11033
, , , ,[6] Cohomology of Groups, Springer-Verlag, 1982. | MR 672956 | Zbl 0584.20036
,[7] Tamagawa numbers for motives with (noncommutative) coefficients, Documenta Mathematica 6 (2001) 501-570. | MR 1884523 | Zbl 1052.11077
, ,[8] On the equivariant Tamagawa number conjecture for Tate motives, Invent. Math. 153 (2003) 303-359. | MR 1992015 | Zbl 02001021
, ,[9] Sur les représentations ℓ-adiques attachées aux formes modulaires de Hilbert, C. R. Acad. Sci., Paris 296 (1983) 629-632. | MR 705677 | Zbl 0537.10018
,[10] Iwasawa theory for the symmetric square of an elliptic curve, J. Reine Angew. Math. 375/376 (1987) 104-156. | MR 882294 | Zbl 0609.14013
, ,[11] On the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 39 (1977) 223-251. | MR 463176 | Zbl 0359.14009
, ,[12] Théorie d'Iwasawa des représentations de de Rham d'un corps local, Ann. of Math. (2) 148 (2) (1998) 485-571. | MR 1668555 | Zbl 0928.11045
,[13] Modularity of certain potentially Barsotti-Tate Galois representations, J. AMS 12 (1999) 521-567. | MR 1639612 | Zbl 0923.11085
, , ,[14] Fermat's Last Theorem, in: Current Development in Mathematics, International Press, 1995, pp. 1-154. | MR 1474977 | Zbl 0877.11035
, , ,[15] Formes modulaires et représentations ℓ-adiques, in: Séminaire Bourbaki 1968/1969, exposé 255, Lecture Notes in Math., vol. 179, 1969, pp. 139-172. | Numdam | Zbl 0206.49901
,[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. | MR 349635 | Zbl 0271.14011
,[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. | MR 546622 | Zbl 0449.10022
,[18] Les schémas de modules de courbes elliptiques, in: Lecture Notes in Math., vol. 349, 1973, pp. 143-316. | MR 337993 | Zbl 0281.14010
, ,[19] Explicit construction of universal deformation rings, in: Elliptic Curves, Modular Forms and Fermat's Last Theorem, International Press, Cambridge, 1995, pp. 313-326. | MR 1638482 | Zbl 0907.13010
, ,[20] Congruence primes for cusp forms of weight , Astérisque 196-197 (1991) 205-213. | MR 1141459 | Zbl 0783.11022
,[21] The refined conjecture of Serre, in: Elliptic Curves, Modular Forms and Fermat's Last Theorem, International Press, Cambridge, 1995, pp. 22-37. | MR 1363493 | Zbl 0853.11031
,[22] On deformation rings and Hecke rings, Annals of Math. 144 (1996) 137-166. | MR 1405946 | Zbl 0867.11032
,[23] An extension of Wiles' results, in: Modular Forms and Fermat's Last Theorem, Springer-Verlag, 1997, pp. 475-489. | MR 1638490 | Zbl 0917.11021
,[24] The Taylor-Wiles construction and multiplicity one, Invent. Math. 128 (1997) 379-391. | MR 1440309 | Zbl 0916.11037
,[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. | MR 1262939 | Zbl 0847.11025
, ,[27] Lifting modular mod ℓ representations, Duke Math. J. 74 (1994) 253-269. | MR 1272977 | Zbl 0809.11025
, ,[28] On the modularity of certain 2-adic Galois representations, Duke Math. J. 109 (2001) 319-382. | MR 1845182 | Zbl 1015.11020
,[29] Dimitrov, M., Galois representations modulo p and cohomology of Hilbert modular varieties, Prépub. Math. de l'Univ. Paris 13, 2004-02. | MR 2172950
[30] Serre's conjecture, in: Modular Forms and Fermat's Last Theorem, Springer-Verlag, 1997, pp. 209-242. | MR 1638480 | Zbl 0918.11023
,[31] Crystalline cohomology and p-adic étale cohomology, in: Algebraic Analysis, Geometry and Number Theory, The John Hopkins University Press, 1989, pp. 25-80. | MR 1463696 | Zbl 0805.14008
,[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. | MR 1079004 | Zbl 0711.14001
,[34] A finiteness theorem for the symmetric square of an elliptic curve, Invent. Math. 109 (1992) 307-327. | MR 1172693 | Zbl 0781.14022
,[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. | MR 2088713 | Zbl 1070.11025
,[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. | MR 563472 | Zbl 0429.14016
,[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. | MR 657238 | Zbl 0544.14016
,[38] Valeurs spéciales des fonctions L des motifs, in: Séminaire Bourbaki, exposé 751, février 1992, Astérisque, vol. 206, 1992, pp. 205-249. | Numdam | MR 1206069 | Zbl 0799.14006
,[39] Construction de représentations p-adiques, Ann. Sci. Éc. Norm. Sup. 15 (1982) 547-608. | Numdam | MR 707328 | Zbl 0579.14037
, ,[40] Geometric Galois representations, in: Elliptic Curves, Modular Forms and Fermat's Last Theorem, International Press, 1995, pp. 41-78. | MR 1363495 | Zbl 0839.14011
, ,[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. | MR 1265546 | Zbl 0821.14013
, ,[42] Fujiwara, K., Deformation rings and Hecke algebras in the totally real case, preprint. | MR 1041221
[43] A relation between automorphic representations of and , Ann. Sci. Éc. Norm. Sup., IV. Ser. 11 (1978) 471-542. | Numdam | MR 533066 | Zbl 0406.10022
, ,[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 680785
,[45] Heegner points and derivatives of L-series, Invent. Math. 84 (1986) 225-320. | MR 833192 | Zbl 0608.14019
, ,[46] The Tame Fundamental Group of a Formal Neighbourhood of a Divisor with Normal Crossings on a Scheme, Springer-Verlag, 1971. | MR 316453 | Zbl 0216.33001
, ,[47] General Selmer groups and critical values of Hecke L-functions, Math. Ann. 297 (1993) 221-233. | MR 1241803 | Zbl 0789.14018
,[48] On the Bloch-Kato conjecture for Hecke L-functions, J. Number Theory 57 (1996) 340-365. | MR 1382756 | Zbl 0869.11055
,[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. | MR 463157 | Zbl 0367.14001
,[51] Congruences of cusp forms and special values of their zeta functions, Invent. Math. 63 (1981) 225-261. | MR 610538 | Zbl 0459.10018
,[52] Bloch-Kato conjecture and main conjecture of Iwasawa theory for Dirichlet characters, Duke Math. J. 119 (2003) 393-464. | MR 2002643 | Zbl 1044.11095
, ,[53] Mixed Motives and Algebraic K-theory, Lect. Notes in Math., vol. 1400, Springer, 1990. | MR 1043451 | Zbl 0691.14001
,[54] Logarithmic structures of Fontaine-Illusie, in: Algebraic Analysis, Geometry and Number Theory, The John Hopkins University Press, 1989, pp. 191-224. | MR 1463703 | Zbl 0776.14004
,[55] Iwasawa theory and p-adic Hodge theory, Kodai Math. J. 16 (1993) 1-31. | MR 1207986 | Zbl 0798.11050
,[56] Euler systems, Iwasawa theory and Selmer groups, Kodai Math. J. 22 (1999) 313-372. | MR 1727298 | Zbl 0993.11033
,[57] The Tamagawa number conjecture for CM elliptic curves, Invent. Math. 143 (2001) 571-627. | MR 1817645 | Zbl 01586347
,[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. | MR 984214 | Zbl 0681.14016
,[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 0791.14019
, ,[60] Complete intersections and Gorenstein rings, in: Elliptic Curves, Modular Forms and Fermat's Last Theorem, International Press, Cambridge, 1995. | MR 1363497 | Zbl 0860.13012
,[61] An introduction to the deformation theory of Galois representations, in: Modular Forms and Fermat's Last Theorem, Springer-Verlag, 1997, pp. 243-311. | MR 1638481 | Zbl 0901.11015
,[62] Class fields of abelian extensions of , Invent. Math. 76 (1984) 179-330. | MR 742853 | Zbl 0545.12005
, ,[63] Modular Forms, Springer-Verlag, 1989. | MR 1021004 | Zbl 0701.11014
,[64] On the p-adic height of Heegner cycles, Math. Ann. 302 (4) (1995) 609-686. | MR 1343644 | Zbl 0841.11025
,[65] On a convolution of L-series, Invent. Math. 7 (1969) 297-312. | MR 246819 | Zbl 0205.50902
,[66] Théorie d'Iwasawa des représentations p-adiques sur un corps local, Invent. Math 115 (1994) 81-149. | MR 1248080 | Zbl 0838.11071
,[67] Fonctions L p-adiques des représentations p-adiques, Astérisque 229 (1995). | MR 1327803 | Zbl 0845.11040
,[68] Congruence relations between modular forms, Proc. ICM 17 (1983) 503-514. | MR 804706 | Zbl 0575.10024
,[69] Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication, Invent. Math. 89 (1987) 527-560. | MR 903383 | Zbl 0628.14018
,[70] The “main conjecture” of Iwasawa theory for imaginary quadratic fields, Invent. Math. 103 (1991) 25-68. | Zbl 0737.11030
,[71] Modular forms and p-adic Hodge theory, Invent. Math. 129 (1997) 607-620. | MR 1465337 | Zbl 0877.11034
,[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. | MR 939477 | Zbl 0656.10023
,[74] Modular forms and de Rham cohomology; Atkin-Swinnerton-Dyer congruences, Invent. Math. 79 (1985) 49-77. | MR 774529 | Zbl 0553.10023
,[75] Motives for modular forms, Invent. Math. 100 (1990) 419-430. | MR 1047142 | Zbl 0760.14002
,[76] Géométrie algébrigue et géométrie analytique, Ann. Inst. Fourier 6 (1956) 1-42. | Numdam | MR 82175 | Zbl 0075.30401
,[77] Local Fields, Springer-Verlag, 1979. | MR 554237 | Zbl 0423.12016
,[78] Sur les représentations modulaires de degré 2 de , Duke Math. J. 54 (1987) 179-230. | MR 885783 | Zbl 0641.10026
,[79] Introduction to the Arithmetic Theory of Automorphic Functions, Iwanami Shoten and Princeton University Press, 1971. | MR 314766 | Zbl 0221.10029
,[80] On the holomorphy of certain Dirichlet series, Proc. London Math. Soc. 31 (1975) 79-98. | MR 382176 | Zbl 0311.10029
,[81] On the periods of modular forms, Math. Ann. 229 (1977) 211-221. | MR 463119 | Zbl 0363.10019
,[82] Ordinary representations and modular forms, Proc. Nat. Acad. Sci. USA 94 (20) (1997) 10520-10527. | MR 1471466 | Zbl 0924.11044
, ,[83] Residually reducible representations and modular forms, IHÉS Publ. 89 (1999) 5-126, (2000). | Numdam | MR 1793414 | Zbl 1005.11030
, ,[84] Special values of zeta functions and Eisenstein series of half integral weight, Amer. J. Math. 102 (1980) 219-240. | MR 564472 | Zbl 0433.10015
,[85] Evaluation of the symmetric square at the near center point, Amer. J. Math. 111 (1989) 585-598. | MR 1011550 | Zbl 0705.11027
,[86] Ring theoretic properties of certain Hecke algebras, Annals of Math. 141 (1995) 553-572. | MR 1333036 | Zbl 0823.11030
, ,[87] p-adic étale cohomology and crystalline cohomology in the semi-stable reduction case, Invent. Math. 137 (2000) 233-411. | MR 1705837 | Zbl 0945.14008
,[88] Modular elliptic curves and Fermat's Last Theorem, Annals of Math. 141 (1995) 443-551. | MR 1333035 | Zbl 0823.11029
,[89] Heights of Heegner cycles and derivatives of L-series, Invent. Math. 130 (1997) 99-152. | MR 1471887 | Zbl 0882.11029
,