Taylor, Richard
Galois representations
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6 : Tome 13 (2004) no. 1 , p. 73-119
Zbl 1074.11030 | MR 2060030 | 3 citations dans Numdam
URL stable : http://www.numdam.org/item?id=AFST_2004_6_13_1_73_0

Bibliographie

[A] Artin (E.) , Zur Theorie der L-Reihen mit allgemeinen Gruppencharakteren , Abh. Math. Sem. Univ. Hamburg 8, p. 292-306 (1930). JFM 56.0173.02

[AC] Arthur (J. ) and Clozel (L.), Simple algebras, base change and the advanced theory of the trace formula, Annals of Math. Studies 120, PUP (1989). MR 1007299 | Zbl 0682.10022

[Berg] Berger ( L.), Représentations p-adiques et équations différentielles , Invent. math. 148, p. 219-284 (2002). MR 1906150 | Zbl 01777245

[Bert] Berthelot ( P.), Altérations de variétés algébriques (d'après A.J.de Jong, Astérisque 241, p. 273-311 (1997). Numdam | MR 1472543 | Zbl 0924.14007

[BCDT] Breuil ( C.), Conrad (B.), Diamond (F.) and Taylor (R.), On the modularity of elliptic curves over Q, J.A.M.S. 14, p. 843-939 (2001). MR 1839918 | Zbl 0982.11033

[BFH] Bump (D. ), Friedberg (S.) and Hoffstein (J.), Nonvanishing theorems for L-functions of modular forms and their derivatives, Invent. math. 102, p. 543-618 (1990). MR 1074487 | Zbl 0721.11023

[BK] Bloch (S.) and Kato ( K.), L-functions and Tamagawa numbers of motives , in "The Grothendieck Festschrift I", Birkauser (1990). MR 1086888 | Zbl 0768.14001

[Br] Brauer (R.) , On Artin's L-series with general group characters, Ann. Math. (2) 48, p. 502-514 (1947). MR 20105 | Zbl 0029.01503

[BSD] Birch (B.) and Swinnerton-Dyer (P.), Notes on elliptic curves II, J. Reine Angew. Math. 218, p. 79-108 (1965). MR 179168 | Zbl 0147.02506

[BT] Buzzard (K. ) and Taylor ( R.), Companion forms and weight one forms, Annals of math 149, p. 905-919 (1999). MR 1709306 | Zbl 0965.11019

[CDT] Conrad ( B.), Diamond (F.) and Taylor (R.), Modularity of certain potentially Barsotti-Tate Galois representations, JAMS 12, p. 521-567 (1999). MR 1639612 | Zbl 0923.11085

[Cl1] Clozel (L.) , Motifs et formes automorphes : applications du principe de fonctorialité, in "Automorphic forms, Shimura varieties and L-functions I" , Academic Press (1990). MR 1044819 | Zbl 0705.11029

[Cl2] Clozel ( L.), Représentations Galoisiennes associées aux representations automorphes autoduales de GL(n, Pub. Math. IHES 73, p. 97-145 (1991). Numdam | MR 1114211 | Zbl 0739.11020

[CPS1] Cogdell ( J.) and Piatetski-Shapiro (I.), Converse theorems for GLn, Publ. Math. IHES 79, p. 157-214 (1994). Numdam | MR 1307299 | Zbl 0814.11033

[CPS2] Cogdell ( J.) and Piatetski-Shapiro (I.), Converse theorems for GLn II, J. reine angew. Math. 507, p. 165-188 (1999). MR 1670207 | Zbl 0912.11022

[De1] Deligne (P. ) , Les constantes des équations fonctionnelles des fonctions L, in LNM 349, Springer ( 1973). MR 349635 | Zbl 0271.14011

[De2] Deligne (P. ) , Courbes elliptiques : formulaire d'après Tate, in "Modular functions of one variable IV", LNM 476, Springer (1975). MR 387292

[De3] Deligne ( P.), La conjecture de Weil I, Publ. Math. IHES 43, p. 273-307 (1974). Numdam | MR 340258

[Dia] Diamond ( F.), The Taylor-Wiles construction and multiplicity one, Invent. Math. 128, p. 379-391 (1997). MR 1440309 | Zbl 0916.11037

[Dix] Dixniier (J. ) , Algèbres enveloppantes, Gauthier Villars (1974).

[Dr] Drinfeld ( V.), Proof of the global Langlands conjecture for GL(2) over a function field, Funct. anal. and its appl. 11, p. 223-225 (1977). MR 498489 | Zbl 0423.12010

[Fa] Faltings ( G.), Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. math. 73, p. 349-366 (1983). Zbl 0588.14026

[Fo1] Fontaine (J.-M. ), talk at "Mathematische Arbeitstagung 1988 ", Maz-Planck-Institut für Mathematik preprint no. 30 of 1988.

[Fo2] Fontaine ( J.-M.), Le corps des périodes p-adiques, Astérisque 223, p. 59-111 (1994). MR 1293971 | Zbl 0940.14012

[Fo3] Fontaine ( J.-M.), Représentations p-adiques semi-stables , Astérisque 223, p. 113-184 (1994). MR 1293972 | Zbl 0865.14009

[Fo4] Fontaine ( J.-M.), Représentations l-adiques potentiellement semi-stables, Astérisque 223, p. 321-347 (1994). MR 1293977 | Zbl 0873.14020

[FM] Fontaine (J.-M. ) and Mazur (B.), Geometric Galois representations, in Elliptic curves, modular forms and Fermat's last theorem (J.Coates and S.-T.Yau eds.), International Press (1995). MR 1363495 | Zbl 0839.14011

[G] Grothendieck ( A.), Formule de Lefschetz et rationalité des fonctions L, in "Dix exposés sur la cohomologie des schémas ", North-Holland (1968). MR 476737 | Zbl 0197.47102

[GeJ] Gelbart ( S.) and Jacquet (H.), A relation between automorphic representations of GL(2) and GL(3, Ann. Sci. ENS 11, p. 471-552 (1978). Numdam | MR 533066 | Zbl 0406.10022

[GoJ] Godenient and Jacquet (H.), Zeta functions of simple algebras, LNM 260, Springer (1972). MR 374100 | Zbl 0244.12011

[GZ] Gross (B. ) and Zagier (D.), Heegner points and derivatives of L-series, Invent. math. 84, p. 225-320 (1986). MR 833192 | Zbl 0608.14019

[Har] Harris (M.) , The local Langlands conjecture for GL(n) over a p-adic field, n < p, Invent. Math. 134, p. 177-210 (1998). Zbl 0921.11060

[Hec] Hecke (E.) , Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung I, II, Math. Ann. 114, p. 1-28 and p. 316-351 (1937). JFM 63.0339.03 | MR 1513122 | Zbl 0015.40202

[Hen1] Henniart ( G.), On the local Langlands conjecture for GL(n): the cyclic case, Ann. of Math. 123, 145-203 (1986). MR 825841 | Zbl 0588.12010

[Hen2] Henniart ( G.), Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adiques, Invent. math. 139, p. 439-455 (2000). MR 1738446 | Zbl 1048.11092

[Her] Herbrand ( J.), Sur les classes des corps circulaires, J. Math. Pures Appl. 11, p. 417-441 (1932). JFM 58.0180.02

[HT] Harris (M.) and Taylor ( R.), The geometry and cohomology of some simple Shimura varieties, PUP (2001). Zbl 1036.11027

[Ih] Ihara (Y.) , On modular curves over finite fields, in " Proceedings of an international colloquium on discrete subgroups of Lie groups and applications to moduli" OUP (1975 ). MR 399105 | Zbl 0343.14007

[Il] Illusie ( L.), Cohomologie de de Rham et cohomologie étale p-adique, Astérisque 189-190, p. 325-374 (1990). Numdam | MR 1099881

[J] Jacquet (H. ) , Principal L-functions of the linear group , in "Automorphic forms, representations and L-functions 2 " AMS (1979). MR 546609 | Zbl 0413.12007

[JL] Jacquet (H. ) and Langlands ( R.), Automorphic forms on GL(2), LNM 114, Springer 1970. MR 401654 | Zbl 0236.12010

[JPSS1] Jacquet ( H.), Piatetski-Shapiro (I.) and Shalika (J.), Automorphic forms on GL(3, Annals of math. 109, p. 169-258 (1979). MR 519356 | Zbl 0401.10037

[JPSS2] Jacquet ( H.), Piatetski-Shapiro ( I.) and Shalika (J.), Relèevement cubique non normal, C. R. Acad. Sci. Paris Sér. I Math. 292 no. 12, p. 567-571 (1981). MR 615450 | Zbl 0475.12017

[JS] Jacquet ( H.) and Shalika (J.), On Euler products and the classification of automorphic representations II, Amer. J. Math. 103, p. 777-815 (1981). MR 623137 | Zbl 0491.10020

[Kol1] Kolyvagin ( V.), Finiteness of E(Q) and Sh(E, Q) for a subclass of Weil curves, Izv. Akad. Nauk SSSR Ser. Mat. 52, p. 522-540 (1988). MR 954295 | Zbl 0662.14017

[Kol2] Kolyvagin ( V.), On the Mordell-Weil group and the Shafarevich-Tate group of modular elliptic curves, in "Proceedings of the Kyoto International Congress of Mathematicians" Math. Soc. Japan (1991). MR 1159231 | Zbl 0749.14012

[Kot] Kottwitz ( R.), On the λ-adic representations associated to some simple Shimura varieties, Invent. math. 108, p. 653-665 (1992). MR 1163241 | Zbl 0765.22011

[Laf] Lafforgue ( L.), Chtoukas de Drinfeld et correspondance de Langlands, Invent. math. 147, p. 1-241 (2002). MR 1875184 | Zbl 1038.11075

[Lan1] Langlands ( R.P. ), On the classification of representations of real reductive groups, mimeographed notes from the IAS, ( 1973 ).

[Lan2] Langlands ( R.P. ), Automorphic representations, Shimura varieties and motives. Ein Märchen. in "Automorphic forms, representations and L-functions II" AMS ( 1979). Zbl 0447.12009

[Lan3] Langlands ( R.P.), Base change for GL(2, Annals of Math. Studies 96, Princeton Univ. Press, Princeton, ( 1980). MR 574808 | Zbl 0444.22007

[Lau] Laumon ( G.), Transformation de Fourier, constantes d'équations fonctionnelles et conjecture de Weil, Publ. math. IHES 65, p. 131-210 (1987). Numdam | MR 908218 | Zbl 0641.14009

[Ma] Mann (W.R.) , Local level raising for GLn, preprint.

[MB] Moret-Bailly ( L.), Groupes de Picard et problèmes de Skolem II, Ann. Sci. ENS 22, p. 181-194 (1989). Numdam | MR 1005158 | Zbl 0704.14015

[Mi] Miyake (T.) , Modular forms, Springer (1989). MR 1021004 | Zbl 0701.11014

[MM] Murty (R.) and Murty ( K.), Mean values of derivatives of modular L-series , Ann. of Math. (2) 133, p. 447-475 (1991). MR 1109350 | Zbl 0745.11032

[P] Pop (F.) , Embedding problems over large fields, Annals of Math. 144, p. 1-34 (1996). MR 1405941 | Zbl 0862.12003

[PS] Piatetski-Shapiro ( I.), Zeta functions of GL(n, Univ. Maryland Techn. Rep. TR 76-46 (1976).

[R1] Ribet (K. ), A modular construction of unramified p-extensions of Q(μp), Invent. math. 34, p. 151-162 (1976). MR 419403 | Zbl 0338.12003

[R2] Ribet (K.) , Congruence relations between modular forms, in "Proceedings of the Warsaw ICM" Polish Scientific Publishers (1984). MR 804706 | Zbl 0575.10024

[Sa] Savitt (D.) , Modularity of some potentially Barsotti-Tate Galois representations , preprint. MR 2004122

[Se1] Serre (J.-P. ) , Corps locaux, Hermann ( 1962). MR 354618

[Se2] Serre (J.-P. ) , Abelian l-adic representations and elliptic curves, Benjamin (1968). MR 263823 | Zbl 0186.25701

[SGA4] Artin (M.) , Grothendieck ( A.) and Verdier (J.L.), Théorie des topos et cohomologie étale des schémas, LNM 269 and 270 and 305, Springer (1972/73). MR 354653

[SGA5] Illusie (L. ) , Cohomologie l-adique et fonctions L, LNM 589 Springer (1977). MR 491704

[SW1] Skinner ( C.) and Wiles (A.), Residually reducible representations and modular forms, Inst. Hautes Etudes Sci. Publ. Math. 89, p. 5-126 (1999). Numdam | MR 1793414 | Zbl 1005.11030

[SW2] Skinner ( C.) and Wiles (A.), Base change and a problem of Serre, Duke Math. J. 107, p. 15-25 (2001). MR 1815248 | Zbl 1016.11017

[SW3] Skinner ( C.) and Wiles (A.), Nearly ordinary deformations of irreducible residual representations, Annales de la Faculté des Sciences de Toulouse X, p. 185-215 (2001). Numdam | MR 1928993 | Zbl 1024.11036

[Tat] Tate (J. ), Number theoretic background, in A. Borel and W.Casselman "Automorphic forms, representations and L-functions" , Proc. Symposia in Pure Math. 33 (2), AMS (1979). MR 546607 | Zbl 0422.12007

[Tay] Taylor (R.) , On the meromorphic continuation of degree two L-functions , preprint available at http://www.math.harvard.edu/ rtaylor.

[Tu] Tunnell ( J.), Artin's conjecture for representations of octahedral type, Bull. AMS 5, p. 173-175 (1981). MR 621884 | Zbl 0475.12016

[TW] Taylor (R. ) and Wiles (A.), Ring theoretic properties of certain Hecke algebras, Annals of Math. 141, p. 553-572 (1995). MR 1333036 | Zbl 0823.11030

[vW] Van Der Waall (R.), On Brauer's induction formula of characters of groups, Arch. Math. 63, p. 208-210 (1994). MR 1287248 | Zbl 0842.20010

[We] Weil (A.) , Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen , Math. Ann. 168, p. 149-156 (1967). MR 207658 | Zbl 0158.08601

[Wi] Wiles (A. ), Modular elliptic curves and Fermat's last theorem, Annals of Math. 141, 443-551 (1995). MR 1333035 | Zbl 0823.11029