References
[An] Anderson, G.:t-motives. Duke Math. J.53, 457–502 (1986)
[Ar-Cl] Arthur, J., Clozel, L.: Base change and the advanced theory of the trace formula. (Ann. Math. Stud. vol. 120) Princeton: Princeton University Press and University of Tokyo Press (1989)
[Art] Artin. M.: Versal deformations and algebraic stacks. Invent. Math.27, 165–189 (1974)
[Be-Ze 1] Bernstein, I.N., Zelevinskii, A.V.: Representations of the group GL(n, F) whereF is a non-archimedean local field. Russ. Math. Surv.31(3), 1–68 (1976)
[Be-Ze 2] Bernstein, I.N. Zelevinskii, A.V.: Induced representations of reductivep-adic groups. I. Ann. Sci. Ec. Norm. Supér., IV. Sér.10, 441–472 (1977)
[Ca] Cartier, P.: Representations of ℘-adic groups: A survey. In: Borel, A., Casselman, W. (eds.) Corvallis conference on Automorphic forms, Representations andL-functions. (Proc. Symp. Pure Math. vol. XXXIII, part 1, pp. 111–156) Providence, RI: Am. Math. Soc. 1979
[Cu-Re] Curtis, C., Reiner, I.: Methods of representation theory: with applications to finite groups and orders, vol. 1. New York: Wiley 1981
[De 1] Deligne, P.: Les constantes des équations fonctionelles des fonctionsL. In: Deligne, P., Kuyk, W. (eds.) Modular functions of one variable II. Antwerpen conference 1972. (Lect. Notes Math., 349, pp. 501–597) Berlin Heidelberg New York: Springer 1973
[De 2] Deligne, P.: La conjecture de Weil II. Publ. Math., Inst. Hautes Étud. Sci.52, 137–252 (1980)
[De 3] Deligne, P.: Formes modulaires et représentations de GL(2). In: Deligne, P., Kuyk, W. (eds.) Modular functions of one variable II. Antwerpen conference 1972. (Lect. Notes Math., vol. 349, pp. 55–105) Berlin Heidelberg New York: Springer 1973
[De-Hu] Deligne, P., Husemoller, D.: Survey of Drinfel'd modules. In: Ribet, K.A. (ed.) Current trends in arithmetical algebraic geometry. (Contemp. Math. vol. 67, pp. 25–91) Providence, RI: Am. Math. Soc. 1987
[De-Ka-Vi] Deligne, P., Kazhdan, D., Vigneras, M.-F.: Représentations des algèbres centrales simplesp-adiques. In: Bernstein, I.N., Deligne, P., Kazhdan, D., Vigneras, M.-F. (eds.) Représentations des groupes réductifs sur un corps local, pp. 33–118. Paris: Hermann 1984
[De-Mu] Deligne, P., Mumford, D.: The irreducibility of the space of curves of given genus. Publ. Math., Inst. Hautes Étud. Sci.36, 75–110 (1969)
[De-Ra] Deligne, P., Rapoport, M.: Les schémas de modules de courbes elliptiques. In: Deligne, P., Kuyk, W. (eds.) Modular functions of one variable II. Antwerpen conference 1972. (Lect. Notes Math., vol. 349, pp. 143–316) Berlin Heidelberg New York: Springer 1973
[Dr 1] Drinfel'd, V.G.: Elliptic modules. Math. USSR, Sb.23, 561–592 (1974)
[Dr 2] Drinfel'd, V.G.: Elliptic modules. II. Math. USSR, Sb.31, 159–170 (1977)
[Dr 3] Drinfel'd, V.G.: Commutative subrings of certain noncommutative rings. Funct. Anal. Appl.11, 9–12 (1977)
[Dr 4] Drinfel'd, V.G.: Letter to H. Carayol (January 12th, 1980)
[Dr 5] Drinfel'd, V.G.: Letter to U. Stuhler. (September 17th, 1985)
[Dr 6] Drinfel'd, V.G.: Varieties of modules ofF-sheaves. Funct. Anal. Appl.21 107–122 (1987)
[Dr 7] Drinfel'd, V.G.: The proof of Petersson's conjecture for GL(2) over a global field of characteristicp. Funct. Anal. Appl.22, 28–43 (1988)
[Dr 8] Drinfel'd, V.G.: Cohomology of compactified manifolds of modules ofF-sheaves of rank 2. J. Soy. Math.46, (no. 1), 1789–1821 (1989)
[Fl-Ka] Flicker, Y., Kazhdan, D.: Geometric Ramanujan conjecture and Drinfeld reciprocity law. In: Aubert, K., Bombieri, E., Goldfeld, D. (eds.) Number theory, trace formulas and discrete groups, pp. 201–218. New York London: Academic Press 1989
[Go-Ja] Godement, R., Jacquet, H.: Zeta functions of simple algebras. (Lect. Notes Math., 260) Berlin Heidelberg New York: Springer 1972
[Gr] Grayson, D.R.: Finite generation ofK-groups of a curve over a finite field (after D. Quillen). In: Dennis, R.K. (ed.). Algebraic K-Theory. Proceedings, 1980, Part I. (Lect. Notes Math., vol. 966, pp. 69–90) Berlin Heidelberg New York: Springer 1982
[Gro] Grothendieck, A.: Techniques de construction et théorèmes d'existence en géométrie algébrique IV: Les schémas de Hilbert. Sémin. Bourbaki, exposé 221 (1960/61)
[Ha-Na] Harder, G., Narasimhan, M.S.: On the cohomology of moduli spaces of vector bundles on curves. Math. Ann.212, 215–248 (1975)
[H-C] Harish-Chandra: A submersion principle and its applications. In: Collected papers, vol. IV, pp. 439–446. Berlin Heidelberg New York: Springer 1984
[He 1] Henniart, G.: On the local Langlands conjecture for GL(n): The cyclic case. Ann. Math.123, 145–203 (1986)
[He 2] Henniart, G.: La conjecture de Langlands locale numérique pour GL(n), Ann. Sci. Éc. Norm. Supér., IV Sér21, 497–544 (1988)
[He 3] Henniart, G.: La conjecture de Langlands locale pour GL(3). Mém. Soc. Math. Fr. Nouv. Sér.11/12, 497–544 (1984)
[He 4] Henniart, G.: Le point sur la conjecture de Langlands pour GL(N) sur un corps local. In: Goldstein, C. (ed.). Séminaire de théorie des nombres de Paris 1983–1984. (Prog. Math., vol. 59, pp. 115–131) Boston Basel Stŭttgart: Birkhäuser 1985
[He 5] Henniart, G.: Appendix to this paper
[Her] Herstein, I.N.: Noncommutative rings. Carus Math. Monogr.15 (1968)
[Il] Illusie, L.: Complexe cotangent et déformations. I, II. (Lect. Notes Math., vols. 239, 283) Berlin Heidelberg New York: Springer 1971, 1973
[Ja-Pi-Sh 1] Jacquet, H., Piatetski-Shapiro, I., Shalika, J.: Automorphic forms on GL3. I, II. Ann. Math.109, 169–258 (1979)
[Ja-Pi-Sh 2] Jacquet, H., Piatetski-Shapiro, I., Shalika, J.: Rankin-Selberg convolutions. Am. J. Math.105, 367–483 (1983)
[Ja-Sh 1] Jacquet, H., Shalika, J.: Conducteur des représentations du groupe linéaire. Math. Ann.256, 199–214, (1979)
[Ja-Sh 2] Jacquet, H., Shalika, J.: On Euler products and the classification of automorphic representations. I. Am. J. Math.103, 499–558 (1981); II. Am. J. Math.103, 777–815 (1981)
[Ka] Kazhdan, D.: An introduction to Drinfeld's “shtuka”. In: Borel, A., Casselman W. (eds.) Corvallis conference on Automorphic forms, Representations andL-functions. (Proc. Symp. Pure Math. vol. XXXIII, part 2, pp. 347–356) Providence, RI: Am. Math. Soc. 1979
[Ko] Koch, H.: Eisensteinsche Polynomfolgen und Arithmetik in Divisionsalgebren über lokalen Körpern. Math. Nachr.104, 229–251 (1981)
[Kot 1] Kottwitz, R.: Sign changes in harmonic analysis on reductive groups. Trans. Am. Math. Soc.278, 289–297 (1983)
[Kot 2] Kottwitz, R.: Tamagawa numbers. Ann. Math.127, 629–646 (1988)
[Kot 3] Kottwitz, R.: On the λ-adic representations associated to some simple Shimura varieties, Invent. math.108, 653–665 (1992)
[La] Langlands, R.P.: Euler Products. Yale University Press 1971
[Lan] Langton, S.: Valuative criteria for families of vector bundles on algebraic varieties. Ann. Math.101, 215–248 (1975)
[Lau 1] Laumon, G.: Transformation de Fourier, constantes d'équations fonctionelles et conjecture de Weil. Publ. Math., Inst. Hautes Étud. Sci.65, 131–210 (1987)
[Lau 2] Laumon, G.: Cohomology with compact supports of Drinfel'd modular varieties. Part I. Prépublications (91-01), pp. 1–201. Orsay: Université de Paris-Sud 1991
[Mo] Morris, L.: Eisenstein series for reductive groups over global function fields. I. The cusp form case. Can. J. Math.34, 91–168 (1982)
[Mo-Wa] Moeglin, C., Waldspurger, J.-L.: Le spectre résiduel de GL(n), Ann. Sci. Éc. Norm. Supér., IV. Sér.22, 605–674 (1989)
[Mu] Mustafin, G.: Nonarchimedian uniformization. Math. USSR, Sb.34, 187–214 (1978)
[Ok-Sch-Sp] Okonek, C., Schneider, M., Spindler, H.: Vector bundles on complex projective spaces. Boston Basel Stuttgart: Birkhäuser 1980
[Ra] Rapoport, M.: On the bad reduction of Shimura varieties. In: Clozel, L., Milne, J. (eds.) Automorphic forms, Shimura varieties andL-functions, vol. II. (Perspect. Math., vol. 11, pp. 253–321) Boston: Academic Press 1990
[Re] Reiner, I.: Maximal orders. New York London: Academic Press 1975
[Ro] Rogawski, J.: Representations of GL(n) and division algebras over ap-adic field, Duke Math. J.50, 161–196 (1983)
[Se] Seshadri, C.S.: Fibrés vectoriels sur les courbes algébriques (redigée par J.-M. Drezet). Astérisque96 (1982)
[Sh] Shalika, J.: The multiplicity one theorem for GL(n). Ann. Math.100, 171–193 (1974)
[Sha] Shahidi, F.: On certainL-functions. Am. J. Math.103, 297–355 (1981)
[St] Stuhler, U.:P-adic homogeneous spaces and moduli problems. Math. Z.192, 491–540 (1986)
[Ta] Tadič, M.: On the classification of irreducible unitary representations of GL(n) and the conjectures of Bernstein and Zelevinsky (non-archimedian case). Ann. Sci. Éc. Norm. Supér., IV. Sér.19, 335–382 (1986)
[Tat] Tate, J.: Local constants. In: Fröhlich, A. (ed.) Algebraic number fields, Durham conference, pp. 89–131 New York London: Academic Press 1977
[Wa] Wang, S.: On the commutator group of a simple algebra. Am. J. Math.72, 323–334 (1950)
[We]) Weil, A.: Basic number theory. Berlin Heidelberg New York: Springer 1967
[SGA 4, vol. III] Artin, M., Grothendieck, A., Verdier, J.-L.: Théorie des topos et cohomologie étale des schémas. (Lect. Notes Math., vol. 305) Berlin Heidelberg New York: Springer 1973
[SGA5] Grothendieck, A.: Cohomologiel-adique et fonctionsL. (Lect. Notes Math., vol. 589) Berlin Heidelberg New York: Springer 1977
[SGA 7 II] Deligne, P., Katz, N.: Groupes de monodromie en géométrie algébrique. (Lect. Notes Math., vol. 340) Berlin Heidelberg New York: Springer 1973
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Oblatum 11-XI-1991 & 16-XII-1992
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Laumon, G., Rapoport, M. & Stuhler, U. \(D\)-elliptic sheaves and the langlands correspondence. Invent Math 113, 217–338 (1993). https://doi.org/10.1007/BF01244308
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DOI: https://doi.org/10.1007/BF01244308