La conjecture de Sato-Tate [d'après Clozel, Harris, Shepherd-Barron, Taylor]

Carayol, Henri

Séminaire Bourbaki - Volume 2006/2007 - Exposés 967-981, Astérisque, no. 317 (2008), Exposé no. 977, 47 p.

@incollection{AST_2008__317__345_0,
     author = {Carayol, Henri},
     title = {La conjecture de {Sato-Tate} [d'apr\`es {Clozel,} {Harris,} {Shepherd-Barron,} {Taylor]}},
     booktitle = {S\'eminaire Bourbaki - Volume 2006/2007  - Expos\'es 967-981},
     series = {Ast\'erisque},
     note = {talk:977},
     pages = {345--391},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {317},
     year = {2008},
     mrnumber = {2487739},
     zbl = {1230.11073},
     language = {fr},
     url = {http://www.numdam.org/item/AST_2008__317__345_0/}
}

TY  - CHAP
AU  - Carayol, Henri
TI  - La conjecture de Sato-Tate [d'après Clozel, Harris, Shepherd-Barron, Taylor]
BT  - Séminaire Bourbaki - Volume 2006/2007  - Exposés 967-981
AU  - Collectif
T3  - Astérisque
N1  - talk:977
PY  - 2008
SP  - 345
EP  - 391
IS  - 317
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2008__317__345_0/
LA  - fr
ID  - AST_2008__317__345_0
ER  -

%0 Book Section
%A Carayol, Henri
%T La conjecture de Sato-Tate [d'après Clozel, Harris, Shepherd-Barron, Taylor]
%B Séminaire Bourbaki - Volume 2006/2007  - Exposés 967-981
%A Collectif
%S Astérisque
%Z talk:977
%D 2008
%P 345-391
%N 317
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2008__317__345_0/
%G fr
%F AST_2008__317__345_0

Carayol, Henri. La conjecture de Sato-Tate [d'après Clozel, Harris, Shepherd-Barron, Taylor], dans Séminaire Bourbaki - Volume 2006/2007  - Exposés 967-981, Astérisque, no. 317 (2008), Exposé no. 977, 47 p. http://www.numdam.org/item/AST_2008__317__345_0/

Bibliographie
Cité par

[1] J. Arthur & L. Clozel - Simple algebras, base change, and the advanced theory of the trace formula, Annals of Mathematics Studies, vol. 120, Princeton University Press, 1989. | MR | Zbl

[2] F. Beukers & G. Heckman - Monodromy for the hypergeometric function $_{n} F_{n - 1}$ , Invent. Math. 95 (1989), p. 325-354. | DOI | EuDML | MR | Zbl

[3] H. Carayol - Formes modulaires et représentations galoisiennes à valeurs dans un anneau local complet, in $p$ -adic monodromy and the Birch and Swinnerton- Dyer conjecture (Boston, MA, 1991), Contemp. Math., vol. 165, Amer. Math. Soc., 1994, p. 213-237. | DOI | MR | Zbl

[4] H. Carayol, Preuve de la conjecture de Langlands locale pour $G L_{n}$ : travaux de Harris-Taylor et Henniart, Séminaire Bourbaki, vol. 1998/99, exp. n° 857, Astérisque 266 (2000), p. 191-243. | EuDML | Numdam | MR | Zbl

[5] L. Clozel - The Sato-Tate conjecture, prépublication. | Zbl

[6] L. Clozel, Représentations galoisiennes associées aux représentations automorphes autoduales de $G L (n)$ , Publ. Math. I.H.É.S. 73 (1991), p. 97-145. | DOI | EuDML | Numdam | MR | Zbl

[7] L. Clozel, On the cohomology of Kottwitz's arithmetic varieties, Duke Math. J. 72 (1993), p. 757-795. | DOI | MR | Zbl

[8] L. Clozel, M. Harris & R. Taylor - Automorphy for some $ℓ$ -adic lifts of automorphic mod $ℓ$ Galois representations, prépublication. | Numdam | Zbl

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

[10] B. Edixhoven - Rational elliptic curves are modular (after Breuil, Conrad, Diamond and Taylor), Séminaire Bourbaki, vol. 1999/2000, exp. n° 871, Astérisque 276 (2002), p. 161-188. | EuDML | Numdam | MR | Zbl

[11] J.-M. Fontaine & G. Laffaille - Construction de représentations $p$ -adiques, Ann. Sci. École Norm. Sup. (4) 15 (1982), p. 547-608. | DOI | EuDML | Numdam | MR | Zbl

[12] K. Fujiwara - Galois deformations and arithmetic geometry of Shimura varieties, in International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zurich, 2006, p. 347-371. | MR | Zbl

[13] A. Genestier & J. Tilouine - Systèmes de Taylor-Wiles pour $G S p (4)$ , Astérisque 302 (2005), p. 177-290, Formes automorphes. II. Le cas du groupe GSp(4). | Numdam | MR | Zbl

[14] M. Harris - Potential automorphy of odd-dimensional symmetric powers of elliptic curves, and applications, prépublication. | DOI | Zbl

[15] M. Harris, N. Shepherd-Barron & R. Taylor - A family of Calabi-Yau varieties and potential automorphy, prépublication. | DOI | Zbl

[16] M. Harris & R. Taylor - The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, vol. 151, Princeton University Press, 2001. | MR | Zbl

[17] E. Hrushovski & A. Pillay - Definable subgroups of algebraic groups over finite fields, J. reine angew. Math. 462 (1995), p. 69-91. | EuDML | MR | Zbl

[18] Y. Ihara - On modular curves over finite fields, in Discrete subgroups of Lie groups and applications to moduli (Internat. Colloq., Bombay, 1973), Oxford Univ. Press, 1975, p. 161-202. | MR | Zbl

[19] N. M. Katz - Exponential sums and differential equations, Annals of Mathematics Studies, vol. 124, Princeton University Press, 1990. | MR | Zbl

[20] M. Kisin - Moduli of flat group schemes and modularity, à paraître dans Ann. of Math. | MR | Zbl

[21] J.-P. Labesse - Cohomologie, stabilisation et changement de base, Astérisque 257 (1999), p. 161. | Numdam | MR | Zbl

[22] C. R. Matthews, L. N. Vaserstein & B. Weisfeiler - Congruence properties of Zariski-dense subgroups. I, Proc. London Math. Soc. (3) 48 (1984), p. 514-532. | DOI | MR | Zbl

[23] L. Moret-Bailly - Groupes de Picard et problèmes de Skolem. I, II, Ann. Sci. École Norm. Sup. (4) 22 (1989), p. 161-179, 181-194. | DOI | EuDML | Numdam | MR | Zbl

[24] M. V. Nori - On subgroups of $G L_{n} (𝐅_{p})$ , Invent. Math. 88 (1987), p. 257-275. | EuDML | MR | Zbl

[25] J. Oesterlé - Travaux de Wiles (et Taylor,... ). II, Séminaire Bourbaki, vol. 1994/95, exp. n° 804, Astérisque 237 (1996), p. 333-355. | EuDML | Numdam | MR | Zbl

[26] J-P. Serre - Abelian $l$ -adic representations and elliptic curves, McGill University lecture notes written with the collaboration of Willem Kuyk and John Labute, W. A. Benjamin, Inc., New York-Amsterdam, 1968. | MR | Zbl

[27] F. Shahidi - On nonvanishing of $L$ -functions, Bull. Amer. Math. Soc. (N.S.) 2 (1980), p. 462-464. | DOI | MR | Zbl

[28] R. Taylor - Automorphy for some $ℓ$ -adic lifts of automorphic mod $ℓ$ Galois représentations II, prépublication. | Numdam | Zbl

[29] R. Taylor, Remarks on a conjecture of Fontaine and Mazur, J. Inst. Math. Jussieu 1 (2002), p. 125-143. | DOI | MR | Zbl

[30] R. Taylor, On the meromorphic continuation of degree two $L$ -functions, Doc. Math. Extra Vol. (2006), p. 729-779. | EuDML | MR | Zbl

[31] R. Taylor & A. Wiles - Ring-theoretic properties of certain Hecke algebras, Ann. of Math. (2) 141 (1995), p. 553-572. | DOI | MR | Zbl

[32] R. Taylor & T. Yoshida - Compatibility of local and global Langlands correspondences, J. Amer. Math. Soc. 20 (2007), p. 467-493. | DOI | MR | Zbl

[33] M.-F. Vignéras - Représentations $l$ -modulaires d'un groupe réductif $p$ -adique avec $l \neq p$ , Progress in Mathematics, vol. 137, Birkhäuser, 1996. | MR | Zbl

[34] A. Wiles - Modular elliptic curves and Fermat's last theorem, Ann. of Math. (2) 141 (1995), p. 443-551. | DOI | MR | Zbl