Le lemme fondamental pour les algèbres de Lie
Publications Mathématiques de l'IHÉS, Volume 111  (2010), p. 1-169
@article{PMIHES_2010__111__1_0,
     author = {Ng\^o, B\h ao Ch\^au},
     title = {Le lemme fondamental pour les alg\`ebres de Lie},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Springer-Verlag},
     volume = {111},
     year = {2010},
     pages = {1-169},
     doi = {10.1007/s10240-010-0026-7},
     zbl = {1200.22011},
     mrnumber = {2653248},
     language = {fr},
     url = {http://www.numdam.org/item/PMIHES_2010__111__1_0}
}
Ngô, Baochâu. Le lemme fondamental pour les algèbres de Lie. Publications Mathématiques de l'IHÉS, Volume 111 (2010) , pp. 1-169. doi : 10.1007/s10240-010-0026-7. http://www.numdam.org/item/PMIHES_2010__111__1_0/

1. A. Altman, A. Iarrobino, and S. Kleiman, Irreducibility of the compactified Jacobian, in Real and Complex Singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976), pp. 1–12. | MR 498546 | Zbl 0415.14014

2. J. Arthur, An introduction to the trace formula, in: Harmonic Analysis, the Trace Formula, and Shimura Varieties, Clay Math. Proc. 4 (2005), Am. Math. Soc., Providence | MR 2192011 | Zbl 1152.11021

3. M. Artin, Algebraic approximation of structures over complete local rings, Inst. Hautes Études Sci. Publ. Math. 36 (1969), p. 23-58 | Numdam | MR 268188 | Zbl 0181.48802

4. A. Beauville, Y. Laszlo, Un lemme de descente, C. R. Acad. Sci. Paris 320 (1995), p. 335-340 | MR 1320381 | Zbl 0852.13005

5. A. Beauville, M. Narasimhan, S. Ramanan, Spectral curves and generalized theta divisor, J. Reine Angew. Math. 398 (1989), p. 169-179 | MR 998478 | Zbl 0666.14015

6. V. Beilinson, A. Drinfeld, Opers, preprint.

7. A. Beilinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Astérisque, 100 (1982). | MR 751966 | Zbl 0536.14011

8. R. Bezrukavnikov, The dimension of the fixed points set on affine flag manifolds, Math. Res. Lett. 3 (1996), p. 185-189 | MR 1386839 | Zbl 0874.20033

9. I. Biswas, S. Ramanan, Infinitesimal study of Hitchin pairs, J. Lond. Math. Soc. 49 (1994), p. 219-231 | MR 1260109 | Zbl 0819.58007

10. S. Bosch, W. Lutkebohmert, M. Raynaud, Neron Models, Ergeb. der Math., 21 (1990), Springer, Berlin | MR 1045822 | Zbl 0705.14001

11. N. Bourbaki, Groupes et algèbres de Lie, (1981), Masson, Paris | Zbl 0483.22001

12. R. Carter, Finite Group of Lie Type, Wiley Classics Library. | MR 1266626 | Zbl 0567.20023

13. C.-L. Chai, J.-K. Yu, Congruences of Néron models for tori and the Artin conductor, Ann. Math. (2) 154 (2001), p. 347-382 | MR 1865974 | Zbl 1098.14014

14. L. Clozel, The fundamental lemma for stable base change, Duke Math. J. 61 (1990), p. 255-302 | MR 1068388 | Zbl 0731.22011

15. R. Cluckers, F. Loeser, Fonctions constructibles exponentielles, transformation de Fourier motivique et principe de transfert, C. R. Acad. Sci. Paris 341 (2005), p. 741-746 | MR 2188869 | Zbl 1081.14032

16. J.-F. Dat, Lemme fondamental et endoscopie, une approche géométrique, Séminaire Bourbaki 940, novembre 2004.

17. O. Debarre, Théorèmes de connexité pour les produits d’espaces projectifs et les grassmanniennes, Am. J. Math. 118 (1996), p. 1347-1367 | MR 1420927 | Zbl 0878.14014

18. P. Deligne, La conjecture de Weil II, Publ. Math. I.H.E.S. 52 (1980), p. 137-252 | Numdam | MR 601520 | Zbl 0456.14014

19. P. Deligne, Décomposition dans la catégorie dérivée, in Motives, Proc. of Symp. in Pure Math., vol. 55.1, pp. 115–128, 1994. | MR 1265526 | Zbl 0809.18008

20. P. Deligne, Communication privée, 2007.

21. M. Demazure and A. Grothendieck, Séminaire de géométrie algébrique du Bois-Marie 3. LNM, vols. 151, 152, 153, Springer.

22. S. Diaz, J. Harris, Ideals associated to Deformations of singular plane curves, Trans. Am. Math. Soc. 309 (1988), p. 433-468 | MR 961600 | Zbl 0707.14022

23. R. Donagi, D. Gaitsgory, The gerb of Higgs bundles, Transform. Groups 7 (2002), p. 109-153 | MR 1903115 | Zbl 1083.14519

24. G. Faltings, Stable G-bundles and projective connections, J. Algebraic Geom. 2 (1993), p. 507-568 | MR 1211997 | Zbl 0790.14019

25. B. Fantechi, L. Göttsche, D. Straten, Euler number of the compactified Jacobian and multiplicity of rational curves, J. Algebraic Geom. 8 (1999), p. 115-133 | MR 1658220 | Zbl 0951.14017

26. M. Goresky, R. Kottwitz, R. Macpherson, Homology of affine Springer fiber in the unramified case, Duke Math. J. 121 (2004), p. 509-561 | MR 2040285 | Zbl 1162.14311

27. M. Goresky, R. Kottwitz, R. Macpherson, Purity of equivalued affine Springer fibers, Represent. Theory 10 (2006), p. 130-146 | MR 2209851 | Zbl 1133.22013

28. M. Goresky, R. Kottwitz, and R. Macpherson, Codimension of root valuation strata, preprint (2006). | MR 2560317 | Zbl 1185.11038

29. A. Grothendieck, Groupes de monodromie en Géométrie algébrique (SGA 7 I), LNM, vol. 288, Springer.

30. A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique IV. Étude locale des schémas et de morphismes de schémas, Publ. Math. I.H.E.S. 20, 24, 28 et 32. | Numdam | Zbl 0135.39701

31. T. Hales, The fundamental lemma for Sp(4), Proc. Am. Math. Soc. 125 (1997), p. 301-308 | MR 1346977 | Zbl 0876.22022

32. T. Hales, A statement of the fundamental lemma, in: Harmonic Analysis, the Trace Formula, and Shimura Varieties, Clay Math. Proc. 4 (2005), Am. Math. Soc., Providence | MR 2192018 | Zbl 1105.22010

33. J. Heinloth, Uniformization of 𝒢 -bundles. A paraître dans Math. Ann. | MR 2640041 | Zbl 1193.14014

34. N. Hitchin, Stable bundles and integrable connections, Duke Math. J. 54 (1987), p. 91-114 | MR 885778 | Zbl 0627.14024

35. D. Kazhdan, On lifting, in: Lie Group Representations, II, Lecture Notes in Math. 1041 (1984), Springer, Berlin | MR 748509 | Zbl 0538.20014

36. D. Kazhdan, G. Lusztig, Fixed point varieties on affine flag manifolds, Isr. J. Math. 62 (1988), p. 129-168 | MR 947819 | Zbl 0658.22005

37. S. Kleiman, Algebraic cycles and Weil conjectures, in: Dix exposés sur la Cohomologie des Schémas, (1968), North-Holland, Amsterdam | MR 292838 | Zbl 0198.25902

38. B. Kostant, Lie group representations on polynomial rings, Am. J. Math. 85 (1963), p. 327-404 | MR 158024 | Zbl 0124.26802

39. R. Kottwitz, Orbital integrals on GL3 , Am. J. Math. 102 (1980), p. 327-384 | MR 564478 | Zbl 0437.22011

40. R. Kottwitz, Unstable orbital integrals on SL(3), Duke Math. J. 48 (1981), p. 649-664 | MR 630589 | Zbl 0477.12019

41. R. Kottwitz, Stable trace formula : cuspidal tempered terms, Duke Math. J. 51 (1984), p. 611-650 | MR 757954 | Zbl 0576.22020

42. R. Kottwitz, Isocristal with additionnal structures, Compos. Math. 56 (1985), p. 201-220 | Numdam | MR 809866 | Zbl 0597.20038

43. R. Kottwitz, Base change for unit elements of Hecke algebras, Compos. Math. 60 (1986), p. 237-250 | Numdam | MR 868140

44. R. Kottwitz, Stable trace formula : elliptic singular terms, Math. Ann. 275 (1986), p. 365-399 | MR 858284 | Zbl 0577.10028

45. R. Kottwitz, Shimura varieties and λ-adic representations, in: Automorphic Forms, Shimura Varieties, and L-functions, Vol. I, Perspect. Math. 10 (1990), Academic Press, Boston | MR 1044820 | Zbl 0743.14019

46. R. Kottwiz, Transfert factors for Lie algebra, Represent. Theory 3 (1999), p. 127-138

47. J.-P. Labesse, Fonctions élémentaires et lemme fondamental pour le changement de base stable, Duke Math. J. 61 (1990), p. 519-530 | MR 1074306 | Zbl 0731.22012

48. J.-P. Labesse, R. Langlands, L-indistinguishability for SL(2), Can. J. Math. 31 (1979), p. 726-785 | MR 540902 | Zbl 0421.12014

49. R. Langlands, Base Change for GL(2), Annals of Mathematics Studies 96 (1980), Princeton University Press, Princeton | MR 574808 | Zbl 0444.22007

50. R.P. Langlands, Les débuts d’une formule des traces stables, in Publications Mathématiques de l’Université Paris VII, vol. 13, Université de Paris VII, U.E.R. de Mathématiques, Paris, 1983. | MR 697567 | Zbl 0532.22017

51. G. Laumon, Fibres de Springer et Jacobiennes compactifiées, in: Algebraic Geometry and Number Theory, Progr. Math. 253 (2006), Birkhäuser Boston, Boston | MR 2263199 | Zbl 1129.14301

52. G. Laumon, Sur le lemme fondamental pour les groupes unitaires, prépublication, arXiv :org/abs/math/0212245 .

53. G. Laumon, L. Moret-Bailly, Champs algébriques, Ergebnisse der Mathematik 39 (2000), Springer, Berlin | MR 1771927 | Zbl 0945.14005

54. G. Laumon, B. C. Ngô, Le lemme fondamental pour les groupes unitaires, Ann. Math. 168 (2008), p. 477-573 | MR 2434884 | Zbl 1179.22019

55. P. Levy, Involutions of reductive Lie algebras in positive characteristic, Adv. Math. 210 (2007), p. 505-559 | MR 2303231 | Zbl 1173.17019

56. D. Mumford, Abelian Varieties. Oxford University Press. | MR 282985 | Zbl 0223.14022

57. B. C. Ngô, Fibration de Hitchin et endoscopie, Inveut. Math 164 (2006), p. 399-453 | MR 2218781 | Zbl 1098.14023

58. B. C. Ngô, Fibration de Hitchin et structure endoscopique de la formule des traces, International Congress of Mathematicians II (2006), Eur. Math. Soc., Zürich | MR 2275642 | Zbl 1096.14029

59. B. C. Ngô, Geometry of the Hitchin fibration. Livre en préparation.

60. B. C. Ngô, Decomposition theorem and abelian fibration. Article d’exposition pour le projet du livre disponible à l’adresse http://fa.institut.math.jussieu.fr/node/44 .

61. Nitsure, Moduli space of semistable pairs on a curve, Proc. Lond. Math. Soc. (3) 62 (1991), p. 275-300 | MR 1085642 | Zbl 0733.14005

62. T. Ono, On Tamagawa numbers, in: Algebraic Groups and Discontinuous Subgroups, Proc. of Symp. in Pure Math 9 (1966), Am. Math. Soc., Providence | MR 209290 | Zbl 0223.20050

63. M. Rapoport, A guide to the reduction of Shimura varieties in Automorphic forms. I, Astérisque 298 (2005), p. 271-318 | MR 2141705 | Zbl 1084.11029

64. M. Raynaud, Communication privée, 2004.

65. J. Rogawski, Automorphic Representations of Unitary Groups in Three Variables, Annals of Math. Studies 123 (1990), Princeton University Press, Princeton | MR 1081540 | Zbl 0724.11031

66. M. Rosenlicht, Some basic theorems on algebraic groups, Am. J. Math. 78 (1956), p. 401-443 | MR 82183 | Zbl 0073.37601

67. H. Saito, Automorphic Forms and Algebraic Extensions of Number Fields (Department of Mathematics, Kyoto University), Lectures in Mathematics 8 (1975), Kinokuniya Book-Store Co., Ltd., Tokyo | MR 406936 | Zbl 0381.10025

68. M. Schöder, Inauguraldissertation, Mannheim 1993.

69. J.-P. Serre, Groupes algébriques et corps de classes, Publications de l’Institut de Mathématique de l’Université de Nancago VII (1959), Hermann, Paris | MR 103191 | Zbl 0318.14004

70. J.-P. Serre, Corps locaux, Publications de l’Institut de Mathématique de l’Université de Nancago VIII (1962), Hermann, Paris | MR 150130 | Zbl 0137.02601

71. D. Shelstad, Orbital integrals and a family of groups attached to a real reductive group, Ann. Sci. École Norm. Supér., 12 (1979). | Numdam | MR 532374 | Zbl 0433.22006

72. N. Spaltenstein, On the fixed point set of a unipotent element on the variety of Borel subgroups, Topology 16 (1977), p. 203-204 | MR 447423 | Zbl 0445.20021

73. T. Springer, Some arithmetical results on semi-simple Lie algebras, Publ. Math. I.H.E.S. 33 (1966), p. 115-141 | Numdam | MR 206171 | Zbl 0156.27002

74. T. Springer, Reductive groups, in: Automorphic Forms, Representations, and L-functions, Proc. Symp. in Pure Math 33-1 (1997), Am. Math. Soc., Providence | MR 546587 | Zbl 0416.20034

75. T. Springer, R. Steinberg, Conjugacy classes, in: Seminar on Algebraic Groups and Related Finite Groups, Lectures Notes in Math. 131 (1970), Springer, Berlin | MR 268192 | Zbl 0249.20024

76. R. Steinberg, Lectures on Chevalley groups, Livre polycopié. | Zbl 1196.22001

77. B. Teissier, Résolution simultanée – I. Famille de courbes, in: Séminaire sur les Singularités des Surfaces, LNM 777 (1980), Springer, Berlin | Numdam | Zbl 0464.14005

78. F. Veldkamp, The center of the universal enveloping algebra of a Lie algebra in characteristic p , Ann. Sci. École Norm. Supér. (4) 5 (1972), p. 217-240 | Numdam | MR 308227 | Zbl 0242.17009

79. J.-L. Waldspurger, Sur les intégrales orbitales tordues pour les groupes linéaires : un lemme fondamental, Can. J. Math. 43 (1991), p. 852-896 | MR 1127034 | Zbl 0760.22026

80. J.-L. Waldspurger, Le lemme fondamental implique le transfert, Compos. Math. 105 (1997), p. 153-236 | MR 1440722 | Zbl 0871.22005

81. J.-L. Waldspurger, Intégrales orbitales nilpotentes et endoscopie pour les groupes classiques non ramifiés, Astérisque, 269. | Zbl 0965.22012

82. J.-L. Waldspurger, Endoscopie et changement de caractéristique, Inst. Math. Jussieu 5 (2006), p. 423-525 | MR 2241929 | Zbl 1102.22010

83. J.-L. Waldspurger, L’endoscopie tordue n’est pas si tordue, Mem. Am. Math. Soc. 194 (2008), p. x+261 | MR 2418405 | Zbl 1146.22016

84. R. Weissauer, A special case of fundamental lemma I–IV, preprint Mannheim (1993).

85. D. Whitehouse, The twisted weighted fundamental lemma for the transfer of automorphic forms from GSp(4). Formes automorphes. II. Le cas du groupe GSp(4), Astérisque 302 (2005), p. 291-436 | MR 2234863 | Zbl 1097.11025