La correspondance de Langlands sur les corps de fonctions

 Access to full text

 Full (PDF)

1. [La 1] L. Lafforgue - Chtoucas de Drinfeld et conjecture de Ramanujan-Petersson, Astérisque, 243 (1997). Zbl0899.11026MR1600006
2. [La 2] L. Lafforgue - Sur la conjecture de Ramanujan-Petersson pour les corps de fonctions. I : Étude géométrique, C. R. Acad. Sci. Paris322 (1996), 605-608. Zbl0864.11026MR1386460
3. [La 3] L. Lafforgue - Sur la conjecture de Ramanujan-Petersson pour les corps de fonctions. II : Étude spectrale, C. R. Acad. Sci. Paris322 (1996), 707- 710. Zbl0864.11027MR1387424
4. [La 4] L. Lafforgue - Sur la dégénérescence des chtoucas de Drinfeld, C. R. Acad. Sci. Paris323 (1996), 491-494. Zbl0884.14008MR1408982
5. [La 5] L. Lafforgue - Compactification de l'isogénie de Lang et dégénérescence des structures de niveau simple des chtoucas de Drinfeld, C. R. Acad. Sci. Paris325 (1997), 1309-1312. Zbl0951.14032MR1490420
6. [La 6] L. Lafforgue - Chtoucas de Drinfeld et applications, dans Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), Doc. Math., (1998), 563-570. Zbl0921.11026MR1648105
7. [La 7] L. Lafforgue - Une compactification des champs classifiant les chtoucas de Drinfeld, J. Amer. Math. Soc.11 (1998), 1001-1036. Zbl1045.11041MR1609893
8. [La 8] L. Lafforgue - Pavages des simplexes, schémas de graphes recollés et compactification des PGLn+1r / PGLr, Invent. Math.136 (1999), 233-271. Zbl0965.14024MR1681089
9. [La 9] L. Lafforgue - La correspondance de Langlands sur les corps de fonctions, manuscrit final, (2000). 
10. [Dr 1] V.G. Drinfeld - Commutative subrings of certain noncommutative rings, Funct. Anal. and its Appl.11 (1977), 9-12. Zbl0368.14011MR476732
11. [Dr 2] V.G. Drinfeld - Proof of the global Langlands conjecture for GL(2) over a function field, Funct. Anal. and its Appl.11 (1977), 223-225. Zbl0423.12010MR498489
12. [Dr 3] V.G. Drinfeld - A proof of Petersson's conjecture for function fields, Uspehi Mat. Nauk32 (1977), 209-210. MR480344
13. [Dr 4] V.G. Drinfeld - Langlands' conjecture for GL(2) over functional fields, dans Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Acad. Sci. Fennica, (1980), 565-574. Zbl0444.12004MR562656
14. [Dr 5] V.G. Drinfeld - Moduli varieties of F-sheaves, Funct. Anal. and its Appl.21 (1987), 107-122. Zbl0665.12013MR902291
15. [Dr 6] V.G. Drinfeld - Proof of the Petersson conjecture for GL(2) over a global field of characteristic p, Funct. Anal. and its Appl.22 (1988), 28- 43. Zbl0662.12012MR936697
16. [Dr 7] V.G. Drinfeld - Cohomology of compactified moduli varieties of F-sheaves of rank 2, J. of Soviet Math.46 (1989), 1789-1821. Zbl0672.14008MR918745
17. [Dr 8] V.G. Drinfeld - On my paper : "Cohomology of compactified moduli varieties of F-sheaves of rank 2", Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), Anal. Teor. Chisel i Teor. Funktsii.9168 (1988), 45-47. MR982482
18. [Ca] H. Carayol - Variétés de Drinfeld compactes, d'après Laumon, Rapoport et Stuhler, dans Séminaire Bourbaki1991/92, Astérisque206, (1992), 369- 409. Zbl0801.14005MR1206074
19. [D-H] P. Deligne, D. Husemoller - Survey of Drinfeld modules, dans Current trends in arithmetical algebraic geometry (Arcata, 1985), Contemp. Math.67, (1987), 25-91. Zbl0627.14026MR902591
20. [Dr 9] V.G. Drinfeld - Elliptic modules, Math. USSR Sbornik23 (1974), 561- 592. Zbl0321.14014MR384707
21. [Dr 10] V.G. Drinfeld - Elliptic modules II, Math. USSR Sbornik31 (1977), 159-170. Zbl0386.20022
22. [Dr 11] V.G. Drinfeld - Number of two-dimensional irreducible representations of the fundamental group of a curve over a finite field, Functional Anal. and its Appl.15 (1982), 294-295. Zbl0479.14017MR639205
23. [F-K] Y. Flicker, D. Kazhdan - Geometric Ramanujan conjecture and Drinfeld reciprocity law, dans Number theory, trace formulas and discrete groups, Academic Press, (1989), 201-218. Zbl0674.10025MR993317
24. [H-K] G. Harder, D. Kazhdan - Automorphic forms on GL2 over function fields (after V. G. Drinfeld), Proc. Sym. Pure Math.33, Part 2 (1979), 357-379. Zbl0442.12011MR546624
25. [Ka] D. Kazhdan - An introduction to Drinfeld's "shtuka", Proc. Sym. Pure Math.33, Part 2 (1979), 347-356. Zbl0411.12007MR546623
26. [Lau 1] G. Laumon - Cohomology of Drinfeld modular varieties, Part I (Geometry, counting of points and local harmonic analysis), Cambridge University Press (1995). Zbl0837.14018MR1381898
27. [Lau 2] G. Laumon - Cohomology of Drinfeld modular varieties, Part II (Automorphic forms, trace formulas and Langlands correspondence), Cambridge University Press (1996). Zbl0870.14016MR1439250
28. [Lau 3] G. Laumon - Drinfeld Shtukas, dans CIME Session "Vector bundles on Curves. New Directions" ( Cetraro, juin 1995), Lecture Notes in Mathematics1649, (1996), 50-109. Zbl0958.11046MR1605028
29. [Lau 4] G. Laumon - The Langlands Correspondence for Function Fields following Laurent Lafforgue, dans Current Developments in Mathematics Conference (Harvard University, novembre 1999). MR1990249
30. [L-R-S] G. Laumon, M. Rapoport ET U. Stuhler - D-elliptic sheaves and the Langlands correspondence, Inv. Math.113 (1993), 217-338. Zbl0809.11032MR1228127
31. [Dr 12] V.G. Drinfeld - Two-dimensional l-adic representations of the fundamental group of a curve over a finite field and automorphic forms on GL(2), Amer. J. Math.105 (1983), 85-114. Zbl0536.14014MR692107
32. [Dr 13] V.G. Drinfeld - Two-dimensional l-adic representations of the Galois group of a global field of characteristic p and automorphic forms on GL(2), J. of Soviet Math.36 (1987), 93-105. Zbl0609.12010
33. [F-G-K-V] E. Frenkel, D. Gaitsgory, D. Kazhdan, K. Vilonen - Geometric realization of Whittaker functions and the Langlands conjecture, J. Amer. Math. Soc.11 (1998), 451-484. Zbl1068.11501MR1484882
34. [Lau 5] G. Laumon - Correspondance de Langlands géométrique pour les corps de fonctions, Duke Math. J.54 (1987), 309-359. Zbl0662.12013MR899400
35. [Lau 6] G. Laumon - Faisceaux automorphes pour GLn : la première construction de Drinfeld, prépublication électronique, réf. alg-geom/9511004. 
36. [De] P. Deligne - La conjecture de Weil. II, Publ. Math. IHES52 (1980), 137-252. Zbl0456.14014MR601520
37. [DC-P] C. De Concini, C. Procesi - Complete symmetric varieties, dans CIME Session "Invariant Theory" (Montecatini), Lecture Notes in Math.996, Springer-Verlag, (1982), 1-44. Zbl0581.14041MR718125
38. [Fa] G. Faltings - Explicit resolution of local singularities of moduli-spaces. Journal für die reine und angewandte Mathematik483 (1997), 183-196. Zbl0871.14012MR1431845
39. [Gr] A. Grothendieck - Formule de Lefschetz et rationalité des fonctions L, Sém. Bourbaki1964/65, exp. n° 279, collection hors série Astérisque9 (1995), 41-55, et dans Dix exposés sur la cohomologie des schémas, North Holland, (1968), 31-45. Zbl0197.47102MR1608788
40. [H-N] G. Harder, M.S. Narasimhan - On the cohomology groups of moduli spaces of vector bundles on curves, Math. Ann. 212 (1975), 215-248. Zbl0324.14006MR364254
41. [H-T] M. Harris, R. Taylor - On the geometry and cohomology of some simple Shimura varieties, Institut de Mathématiques de Jussieu, Prépublication 227, (1999). 
42. [Lak] D. Laksov - Completed quadrics and linear maps, dans Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), Proc. Sympos. Pure Math., 46, Part 2, Amer. Math. Soc., (1987), 371-387. Zbl0679.14030MR927988
43. [Lau 7] G. Laumon - Transformation de Fourier, constantes d'équations fonctionnelles et conjecture de Weil, Publ. Math. I.H.E.S.65 (1987), 131-210. Zbl0641.14009MR908218
44. [L-M] G. Laumon, L. Moret-Bailly - Champs algébriques, Springer-Verlag (1999). MR1771927
45. [Pi] R. Pink - On the calculation of local terms in the Lefschetz-Verdier trace formula and its application to a conjecture of Deligne, Ann. Math.135 (1992), 483-525. Zbl0769.14007MR1166642
46. [SD] B. Saint-Donat - Affine Embeddings, dans Toroidal Embeddings I, Lecture Notes in Math.339, Springer-Verlag, (1973), 1-40. MR354654
47. [Se] J.-P. Serre - Abelian l-Adic Representations and Elliptic Curves, Addison-Wesley (1988). Zbl0709.14002MR1043865
48. [Ar] J. Arthur - A trace formula for reductive groups I : terms associated to classes in G(Q), Duke Math. J.45 (1978), 911-953. Zbl0499.10032MR518111
49. [C-PS] J.W. Cogdell, I.I. Piatetski-Shapiro - Converse theorems for GLn, Publ. Math. IHES79 (1994), 157-214. Zbl0814.11033MR1307299
50. [G-J] R. Godement, H. Jacquet - Zeta functions of simple algebras, Lecture Notes in Math.260, Springer-Verlag, (1972). Zbl0244.12011MR342495
51. [J-PS-S] H. Jacquet, I.I. Piatetski-Shapiro, J.A. Shalika - Rankin-Selberg convolutions, Amer. J. Math.105 (1983), 367-464. Zbl0525.22018MR701565
52. [J-S 1] H. Jacquet, J.A. Shalika - On Euler products and the classification of automorphic representations I, Amer. J. Math.103 (1981), 499-558. Zbl0473.12008MR618323
53. [J-S 2] H. Jacquet, J.A. Shalika - On Euler products and the classification of automorphic representations II, Amer. J. Math.103 (1981), 777-815. Zbl0473.12008MR623137
54. [Lan 1] R.P. Langlands - Problems in the theory of automorphic forms, dans Lectures in modern analysis and applications III, Lecture Notes in Math.170, Springer-Verlag, (1970), 18-61. Zbl0225.14022MR302614
55. [Lan 2] R.P. Langlands - On the functional equations satisfied by Eisenstein series, Lecture Notes in Math.544, Springer-Verlag (1976). Zbl0332.10018MR579181
56. [M-W] C. Moeglin, J.-L. Waldspurger - Décomposition spectrale et séries d'Eisenstein, Une paraphrase de l'Écriture, Birkhäuser (1994). Zbl0794.11022MR1261867
57. [PS 1] I.I. Piatetski-Shapiro - Zeta functions of GL(n), prépublication de l'université du Maryland, (1976). 
58. [PS 2] I.I. Piatetski-Shapiro - Multiplicity one theorem, Proc. Sym. Pure Math.33, Part 1 (1979), 209-212. Zbl0423.22017MR546599
59. [Sh] J.A. Shalika - The multiplicity one theorem for GLn, Ann. of Math.100 (1974), 171-193. Zbl0316.12010MR348047

1. Guy Henniart, Progrès récents en fonctorialité de Langlands