The local Langlands correspondence: notes of (half) a course at the IHP Spring 2000

Harris, Michael

Formes automorphes (I) - Actes du semestre du centre Émile Borel, printemps 2000, Astérisque, no. 298 (2005), pp. 17-145.

MR Zbl

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     author = {Harris, Michael},
     title = {The local {Langlands} correspondence: notes of (half) a course at the {IHP} {Spring} 2000},
     booktitle = {Formes automorphes (I) - Actes du semestre du centre \'Emile Borel, printemps 2000},
     editor = {Tilouine Jacques and Carayol Henri and Harris Michael and Vign\'eras Marie-France},
     series = {Ast\'erisque},
     pages = {17--145},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {298},
     year = {2005},
     mrnumber = {2141702},
     zbl = {1084.11028},
     language = {en},
     url = {http://www.numdam.org/item/AST_2005__298__17_0/}
}

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Harris, Michael. The local Langlands correspondence: notes of (half) a course at the IHP Spring 2000, dans Formes automorphes (I) - Actes du semestre du centre Émile Borel, printemps 2000, Astérisque, no. 298 (2005), pp. 17-145. http://www.numdam.org/item/AST_2005__298__17_0/

Bibliographie
Cité par

[A] J. Arthur - The $L^{2}$ Lefschetz numbers of Hecke operators, Invent. Math. 97 (1989), p. 257-290. | DOI | EuDML | MR | Zbl

[AC] 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, Princeton, NJ, 1989. | Numdam | MR | Zbl

[B] V. G. Berkovich - Vanishing cycles for formal schemes, Invent. Math. 115 (1994), p. 549-571. | DOI | EuDML | MR | Zbl

[BII] V. G. Berkovich, Vanishing cycles for formal schemes, II, Invent Math. 125 (1996), p. 367-390. | DOI | MR | Zbl

[BZ] I. N. Bernstein & A. V. Zelevinsky - Induced representations of reductive $p$ -adic groups I, Ann. scient. Éc. Norm. Sup. 4e série 10 (1977), p. 441-472. | DOI | EuDML | Numdam | MR | Zbl

[Bu] N. Bourbaki - Groupes et algèbres de Lie, Hermann, Paris, 1975, Chap. 7 et 8. | Zbl

[Bo] P. Boyer - Mauvaise réduction de variétés de Drinfel'd et correspondance de Langlands locale, Invent. Math. 138 (1999), p. 573-629. | DOI | MR | Zbl

[BHK] C. Bushnell, G. Henniart & P. Kutzko - Correspondance de Langlands locale pour $G L_{n}$ et conducteurs de paires, Ann. scient. Éc. Norm. Sup. 4e série 31 (1998), p. 537-560. | DOI | EuDML | Numdam | MR | Zbl

[Ca1] H. Carayol - Sur la mauvaise réduction des courbes de Shimura, Compositio Math. 59 (1986), p. 151-230. | EuDML | Numdam | MR | Zbl

[Ca2] H. Carayol, Sur les représentations $ℓ$ -adiques associées aux formes modulaires de Hilbert, Ann. scient. Éc. Norm. Sup. 4e série 19 (1986), p. 409-468. | DOI | EuDML | Numdam | MR | Zbl

[Ca3] H. Carayol, Non-abelian Lubin-Tate theory, in Automorphic Forms, Shimura varieties. and L-functions (L. Clozel & J.S. Milne, eds.), vol. II, Academic Press, New York, 1990, p. 15-39. | MR | Zbl

[C1] L. Clozel - On the limit multiplicities of discrete series representations in spaces of automorphic forms, Invent. Math. 83 (1986), p. 265-284. | DOI | EuDML | MR | Zbl

[C2] L. Clozel, Représentations galoisiennes associées aux représentations automorphes autoduales de $G L (n)$ , Publ. Math. Inst. Hautes Études Sci. 73 (1991), p. 97-145. | DOI | EuDML | Numdam | MR | Zbl

[CL] L. Clozel & J.-P. Labesse - Changement de base pour les représentations coho-mologiques de certains groupes unitaires, Appendix to [L], p. 119-133.

[De1] P. Deligne - Travaux de Shimura, in Séminaire Bourbaki, Lect. Notes in Math., vol. 244, Springer Verlag, 1971. | Numdam | MR | Zbl

[De2] P. Deligne, Les constantes des équations fonctionnelles des fonctions $L$ , in Modular-functions of one variable, II (P. Deligne & W. Kuyk, eds.), Lect. Notes in Math., vol. 349, Springer Verlag, 1973, p. 501-597. | DOI | MR | Zbl

[DKV] P. Deligne, D. Kazhdan & M.-F. Vignéras - Représentations des algèbres centrales simples $p$ -adiques, in Représentations des groupes réductifs sur un corps local (J.-N. Bernstein, P. Deligne, D. Kazhdan & M.-F. Vignéras, eds.), Hermann, Paris, 1984. | MR | Zbl

[Dr] V. G. Drinfel'D - Elliptic Modules, Mat. Sb. (N.S.) 94 (1974), p. 561-592. | DOI | MR | Zbl

[Fa] L. Fargues - Correspondances de Langlands locales dans la cohomologie des espaces de Rapoport-Zink, in Variétés de Shimura, espaces de Rapoport-Zink, et correspondances de Langlands locales, Astérisque, vol. 291, Société Mathématique de France, 2004, thèse de doctorat, Université Paris 7 (2001) | Numdam | Zbl

[F] K. Fujiwara - Rigid geometry, Lefschetz-Verdier trace formula and Deligne's conjecture, Invent. Math. 127 (1997), p. 489-533. | DOI | MR | Zbl

[Ha] G. Harder - Über die Galoiskohomologie halbeinfacher Matrizengruppen. II, Math. Z. 92 (1966), p. 396-415. | DOI | EuDML | MR | Zbl

[H1] M. Harris - Supercuspidal representations in the cohomology of Drinfel'd upper half spaces; elaboration of Carayol's program, Invent. Math. 129 (1997), p. 75-119. | DOI | MR | Zbl

[H2] M. Harris, The local Langlands conjecture for $G L (n)$ over a $p$ -adic field, $n < 1$ , Invent. Math. 134 (1998), p. 177-210. | DOI | MR | Zbl

[H3] M. Harris, Local Langlands correspondences and vanishing cycles on Shimura varieties, in Proceedings of the European Congress of Mathematics (Barcelona, 2000), Progress in Math., vol. 201, Birkhaüser, Basel, 2001, p. 407-427. | DOI | MR | Zbl

[HT] M. Harris & R. Taylor - On the geometry and cohornology of some simple Shimura varieties, Annals of Math. Studies, vol. 151, Princeton University Press, Princecton, NJ, 2001. | MR | Zbl

[HT2] M. Harris & R. Taylor, Deformations of automorphic Galois representations, manuscript, 1998.

[He1] G. Henniart - On the local Langlands conjecture for $G L (n)$ : the cyclic case, Ann. of Math. 123 (1986), p. 145-203. | DOI | MR | Zbl

[He2] G. Henniart, La conjecture de Langlands locale numérique pour $G L (n)$ , Ann. scient. Éc. Norm. Sup. 4e série 21 (1988), p. 497-544. | DOI | EuDML | Numdam | MR | Zbl

[He3] G. Henniart, Une conséquence de la théorie de changement de base pour $G L (n)$ , in Analytic Number Theory, Lect. Notes in Math., vol. 1434, Springer Verlag, 1990, p. 138-142. | DOI | MR | Zbl

[He4] G. Henniart, Caractérisation de la correspondence de Langlands locale par les facteurs $ϵ$ de paires, Invent. Math. 113 (1993), p. 339-350. | DOI | EuDML | MR | Zbl

[He5] G. Henniart, Une preuve simple des conjectures de Langlands pour $G L_{n}$ sur un corps $p$ -adique, Invent. Math. 139 (2000), p. 439-455. | DOI | MR | Zbl

[HH] G. Henniart & H. Herb - Automorphic induction for $G L (n)$ (over local non-archimedean fields), Duke Math. J. 78 (1995), p. 131-192. | DOI | MR | Zbl

[Hida] H. Hida - $p$ -adic Automorphic Forms on Shimura varieties, Springer Monographs in Mathematics, Springer, New York, 2004. | DOI | MR | Zbl

[HG] M. J. Hopkins & B. Gross - Equivariant vector bundles on the Lubin-Tate moduli space, Contemporary Math. 158 (1994), p. 23-88. | DOI | MR | Zbl

[Il] L. Illusie - Autour du théorème de monodromie locale, in Périodes $p$ -adiques, Astérisque, vol. 223, Société Mathématique de France, 1994, p. 9-57. | Numdam | MR | Zbl

[JPSS] H. Jacquet, I. I. Piatetski-Shapiro & J. Shalika - Rankin-Selberg convolutions, Amer. J. Math. 105 (1983), p. 367-483. | DOI | MR | Zbl

[Ka] N. Katz - Serre-Tate local moduli, in Surfaces Algébriques, Lect. Notes in Math., vol. 868, Springer Verlag, 1981, p. 141-143. | MR | Zbl

[KM] N. Katz & B. Mazur - Arithmetic moduli of elliptic curves, Annals of Mathematics Studies, vol. 108, Princeton University Press, Princeton, NJ, 1985. | MR | Zbl

[K1] R. Kottwitz - Stable trace formula: cuspidal tempered terms, Duke Math. J. 51 (1984), p. 611-650. | DOI | MR | Zbl

[K2] R. Kottwitz, Stable trace formula: elliptic singular terms, Math. Ann. 275 (1986), p. 365-399. | DOI | EuDML | MR | Zbl

[K3] R. Kottwitz, Tamagawa Numbers, Ann. of Math. 127 (1988), p. 629-646. | DOI | MR | Zbl

[K4] R. Kottwitz, On the $λ$ -adic representations associated to some simple Shimura varieties, Invent. Math. 108 (1992), p. 653-665. | DOI | EuDML | MR | Zbl

[K5] R. Kottwitz, Points on some Shimura varieties over finite fields, J. Amer. Math. Soc. 5 (1992), p. 373-444. | DOI | MR | Zbl

[K6] R. Kottwitz, Isocrystals with additional structure, Compositio Math. 56 (1985), p. 201-220. | EuDML | Numdam | MR | Zbl

[K7] R. Kottwitz, Isocrystals with additional structure II, Compositio Math. 109 (1997), p. 255-339. | DOI | MR | Zbl

[L] J.-P. Labesse - Cohomologie, stabilisation, et changement de base, Astérisque, vol. 257, Société Mathématique de France, 1999. | Numdam | MR | Zbl

[La] R. P. Langlands - Automorphic representations, Shimura varieties, and motives. Ein Märchen, in Automorphic forms, representations, and $L$ -functions, part 2, Proc. Symp. Pure Math., vol. 33, American Mathematical Society, 1979, p. 205-246. | DOI | MR | Zbl

[LRS] G. Laumon, M. Rapoport & U. Stuhler - $𝒟$ -elliptic sheaves and the Langlands correspondence. Invent. Math. 113 (1993), p. 217-338. | DOI | EuDML | MR | Zbl

[LT] J. Lubin & J. Tate - Formal moduli for one-parameter formal Lie groups, Bull. Soc. math. France 94 (1966), p. 49-59. | DOI | EuDML | Numdam | MR | Zbl

[Ma] E. Mantovan - On certain unitary group Shimura varieties, in Variétés de Shimura, espaces de Rapoport-Zink, et correspondances de Langlands locales, Astérisque, vol. 291, Société Mathématique de France, 2004, Harvard Ph.D. thesis (2002). | MR | Zbl

[Me] W. Messing - The crystals associated to Barsotti-Tate groups: with applications to abelian schemes, Lect. Notes in Math., vol. 264, Springer Verlag, 1972. | MR | Zbl

[Mi1] J. S. Milne - Canonical models of mixed Shimura varieties and automorphic vector bundles, in Automorphic Forms, Shimura varieties, and L-functions (L. Clozel & J.S. Milne, eds.), vol. I, Academic Press, New York, 1990, p. 283-414. | MR | Zbl

[Mi2] J. S. Milne, The points on a Shimura variety modulo a prime of good reduction, in The Zeta Functions of Picard Modular Surfaces (R.P. Langlands & D. Ramakrishnan, eds.), Les publications CRM, Montréal, 1992, p. 151-253. | MR | Zbl

[Mu] D. Mumford - Abelian Varieties, Oxford University Press, 1974. | Zbl

[Oo] F. Oort - Subvarieties of moduli space, Invent. Math. 24 (1974), p. 95-119. | DOI | EuDML | MR | Zbl

[RR] M. Rapoport & M. Richartz - On the classification and specialization of $F$ -isocrystals with additional structure, Compositio Math. 103 (1996), p. 153-181. | EuDML | Numdam | MR | Zbl

[RZ] M. Rapoport & T. Zink - Period Spaces for $p$ -divisible Groups, Annals of Mathematics Studies, vol. 141, Princeton University Press, Princeton, NJ, 1996. | MR | Zbl

[Ro] J. Rogawski - Representations of GL(n) and division algebras over a $p$ -adic field, Duke Math. J. 50 (1983), p. 161-196. | MR | Zbl

[SGA7] A. Grothendieck, P. Deligne & N. Katz - Groupes de monodromie en géométrie algébrique, Lect. Notes in Math., vol. 288, 240, Springer Verlag, 1972, 1973. | MR

[Sh] F. Shahidi - Local coefficients and normalization of intertwining operators for $G L (n)$ , Compositio Math. 48 (1983), p. 271-295. | EuDML | Numdam | MR | Zbl

[SS] P. Schneider & U. Stuhler - Representation theory and sheaves on the Bruhat-Tits building, Publ. Math. Inst. Hautes Études Sci. 85 (1997), p. 97-191. | DOI | EuDML | Numdam | MR | Zbl

[Ta] J. Tate - Classes d'isogénie des variétés abéliennes sur un corps fini, in Séminaire Bourbaki, Lect. Notes in Math., vol. 179, Springer Verlag, 1971, exp. n° 352. | Numdam | MR | Zbl

[V] M.-F. Vignéras - Correspondance de Langlands semi-simple pour $G L (n, F)$ modulo $ℓ \neq p$ , Prépublication, Institut de Mathématiques de Jussieu, 1999.

[Z] A. V. Zelevinsky - Induced representations of reductive $p$ -adic groups II: on irreducible representations of $G L (n)$ , Ann. scient, Éc. Norm. Sup. 4e série 13 (1980), p. 165-210. | DOI | EuDML | Numdam | MR | Zbl

[Zi] T. Zink - Über die schlechte Reduktion einiger Shimuramannigfaltigkeiten, Compositio Math. 45 (1981), p. 15-107. | EuDML | Numdam | MR | Zbl