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References
[An1] G. Anderson: t-Motives, Duke Math. J. 53 (1986), 457–502
[An2] G. Anderson: Notes on t-Motives, Lectures given at the Institute for Advanced Studies, Princeton 1987.
[An3] G. Anderson: A two-dimensional analogue of Stickelberger’s theorem, The Arithmetic of Function Fields (D. Goss, D. Hayes, and M. rosen, eds.), Proc. Workshop Ohio State Univ., June 17–26, 1991, de Gruyter, Berlin and New York, 1992, pp. 51–73
[An4] G. Anderson: Rank one elliptic A-modules and A-harmonic series. Duke Math. J. 73 (1994), 491–542
[Ar-Co-1] E. Arbarello, C. De Concini: On a set of equations characterizing Riemann matrices, Ann. of Math. (2) 120 (1984), 119–140
[Ar-Co-2] E. Arbarello, C. De Concini: Geometrical aspects of the Kadomtsev-Petviashvili equation, Lecture notes in Mathematics 1451, Springer Verlag 1990, p. 95–137.
[Art] M. Artin: Versal deformations and algebraic stacks, Inv. Math. 27, (1974), 165–189
[Ba] H. Bass: Algebraic K-theory, W.A. Benjamin, Inc., New York 1968
[Bo-Gu-Re] S. Bosch, U. Güntzer, R. Remmert. Non-Archimedean Analysis. Berlin-Heidelberg-New York: Springer 1984
[Br-Ti] F. Bruhat, J. Tits: Groupes réductifs sur un corps local. I, Données radicielles valués, Publ. Math. IHES 41, (1972), 5–251.
[Bour] N. Bourbaki: Élements de mathematique, Algèbre commutative, chap. 7: Diviseurs Paris, Hermann 1965.
[Bo-Ca] J.-F. Boutot, H. Carayol: Uniformisation p-adique des courbes de Shimura, Asterisque 196–197, (1991), 45–149
[Bu-Cha] J.L. Burchnall, T.W. Chaundy: Commutative ordinary differential operators, Proc. London Math. Soc. Ser. 2, 21, (1923), 420–440; Proc. Royal Soc. London Ser. A, 118 (1928), 557–583
[Cal] H. Carayol: Non-abelian Lubin-Tate theory, in: Clozel, L., Milne, J.S. (ed), Automorphic forms, Shimura varieties and L-functions vol. II, Persp. in Math. 11, 15–40, Acad. Press Boston (1990)
[Ca2] H. Carayol: Varietés de Drinfeld compactes, (d’après Laumon, Rapoport et Stuhler). Sém. Bourbaki, 44 ème année, 1991–92 Nr. 756
[Carl] L. Carlitz, On certain functions connected with polynomials in a Galois field, Duke Math. J. 1 (1935), 137–168
[Ch] I.V. Cherednik: Uniformization of algebraic curves by discrete subgroups of PGL 2 (k w ) Math. USSR Sbornik, 29, (1976), 55–78
[De-Hu] P. Deligne, D. Husemöller: Survey of Drinfeld modules, Contemp. Math. 67 (1987), 25–91
[De-Mu] P. Deligne, D. Mumford: The irreducibility of the space of curves of given genus, Publ. Math. I.H.E.S., Nr. 36, (1969), 75–110
[De-Ra] P. Deligne, M. Rapoport: Les schémas de modules de courbes elliptiques. In: Modular functions of one variable II, Antwerpen conference 1972, Springer lecture notes in mathematics 349, (1973), 143–316
[Dr1] V.G. Drinfeld: Elliptic modules, Mat. Sb. 94, (1974), 594–627; [English transl. in Math. USSR-Sb. 23 (1976), 561–592]
[Dr2] V.G. Drinfeld: Elliptic modules. II, Mat. Sb. 102, (1974) [English transl. in Math. USSR-Sb. 31 (1977), 159–170
[Dr3] V.G. Drinfeld: Commutative subrings of some noncommutative rings, Funct. Anal. 11 (1977), 11–14
[Dr4] V.G. Drinfeld: Coverings of p-adic symmetric regions. Funct. Anal. Appl. 10 (1976), 107–115.
[Dr5] V.G. Drinfeld: Varieties of modules of F-sheaves, Funct. Anal. and its Appl. 21, (1987), 107–122
[Dr6] V.G. Drinfeld: The proof of Petersson’s conjecture for GL(2) over a global field of characteristic p. Funct. Anal. and its Appl. 22, (1988), 28–43
[Dr7] V.G. Drinfeld: Cohomology of compactified manifolds of modules of F-sheaves of rank 2, Journal of Soviet math., vol. 46, No. 1, (1989), 1789–1821
[Dr8] V.G. Drinfeld: Letter to H. Carayol from 12.1.80
[Fa1] G. Faltings: F-isocrystals on open varieties. Results and conjectures. Grothendieck Festschrift, Progress in Math., Birkhäuser 1990
[Fa2] G. Faltings: The trace formula and Drinfeld’s upper halfplane, Duke Math. J. 76, 1994, 467–481
[Fl-Ka] Y. Flicker, D. Kazhdan: Geometric Ramanujan conjecture and Drinfeld reciprocity law, in: Number theory, trace formulas and discrete groups (K. Aubert, E. Bombieri, D. Goldfeld, (eds), Academic press, (1989), 201–218
[Fr-Pu] J. Fresnel, M. van der Put: Géométrie Analytique Rigide et Applications. Boston: Birkhäuser (1981)
[Gek1] E.-U. Gekeler: On the de Rham isomorphism for Drinfeld modules. J. reine angew. Math. 401, (1989), 188–208
[Gek2] E.-U. Gekeler: De Rham cohomology for Drinfeld modules, Sém. Théorie des Nombres, Paris 1988–1989, Birkhäuser Basel and Boston, (1990), 57–85
[Gen1] A. Genestier: Ramification du revêtement de Drinfeld, Thesè, Université de Paris Sud, Orsay, 1992
[Gen2] A. Genestier: Espaces symétriques de Drinfeld, prepublication, Université de Paris-Sud, Orsay, 1995
[Go-Iw] O. Goldmann, N. Iwahori: The space of p-adic norms. Acta Math. 109, (1963), 137–177
[Go1] D. Goss: The algebraist’s upper half-plane. Bull. AMS 2, (1980), 391–415
[Go2] D. Goss: Drinfeld modules: Cohomology and special functions, Proceedings of Symposia in Pure Mathematics, vol. 55, 1994, part 2, p. 309–362
[Gro-Hop1] B. Cross, M. Hopkins: Equivariant vector bundles on the Lubin-Tate moduli space, Contemp. Math. 158, (1994), 23–88
[Gro-Hop2] B. Gross, M. Hopkins: The rigid analytic period mapping, Lubin-Tate space, and stable homotopy theory, Bull. Amer. Math. Soc. 30, (1994), 76–86
[Groth] A. Grothendieck: Élements de Géometrie Algebrique (EGA), rédigés avec la collaboration de J. Dieudonné, Publ. Math. I.H.E.S., 4, 8, 11, 17, 20, 24, 28, 32, Bures-Sur-Yvette, 1960–1967
[Hur] J. Hurtubise: Algebraic geometry and completely integrable Hamiltonian systems, Canadian Math. Soc., Conference Proceedings vol. 12, 1992, 85–104
[Ka-Ma] N. Katz. B. Mazur: Arithmetic moduli of elliptic curves, Annals of Math. Studies 108, Princeton University Press, 1985.
[Kaz] D. Kazhdan: An introduction to Drinfeld’s “shtuka”, Proc. Sym. Pure Math. 33, part 2, (1979), 347–356
[Ko] N. Koblitz: p-adic numbers, p-adic analysis and Zeta functions, Sec. edition, Springer Verlag, 1984
[Kri] I.M. Krichever: Methods of algebraic geometry in the theory of nonlinear equations, Russ. Math. Surveys 32 (1977), 185–214
[Ku] A. Kurihara: Construction of p-adic unit balls and the Hirzebruch proportionality. Amer. J. Math. 102, (1980), 565–648
[Laf] L. Lafforgue: D-stukas de Drinfeld, Université de Paris Sud, Orsay, 1994
[Lau1] G. Laumon: Sur les modules de Krichever, Preprint
[Lau2] G. Laumon: Cohomology of Drinfeld modular varieties, part I, Cambridge University Press, 1996, Part II, to appear
[Lau-Mo] G. Laumon, L. Moret-Bailly: Champs algébriques; Prépublications de l’université de Paris Sud, 193
[Lau-Ra-Stxxx] G. Laumon, M. Rapoport, U. Stuhler: D-elliptic sheaves and the Langlands correspondence; Inventiones mathematicae 113, 1993, 217–338
[MacL] S. MacLane: Homology, Springer-Verlag, 1967
[Mi] St. Milne: Etale Cohomology, Princeton Mathematical Series, vol. 33, Princeton University Press, Princeton 1980
[Mu1] D. Mumford: An analytic construction of degenerating curves over complete local rings. Compositio Math. 24, (1972), 129–174
[Mu2] D. Mumford: An Algebro-geometric construction of commuting oeprators and of solutions to the Toda lattice equation, Korteweg-de Vries equation and related non-linear equations, (Proc. Internat. Sympos. Alg. Geometry, Kyoto, 1977), Kinokuniy Book Store, Tokyo, (1978), 115–153
[Mu3] D. Mumford: Tata Lectures on Theta II, Birkhäuser-Verlag, Basel, Switzerland, and Cambridge, MA 1984
[Mustxxx] G. Mustafin: Nonarchimedian uniformization, Math. USSR Sbornik 34 (1978), 187–214
[Pr-Se] A. Pressley, G. Segal: Loop Groups, Oxford University press 1986
[Ra] M. Rapoport: On the bad reduction of Shimura varieties, in L. Clozel, J.S. Milne (ed), Persp. in Math. 11, Academic Press, Boston 1990, 253–321
[Ra-Zi] M. Rapoport, Th. Zink: Period spaces for p-divisible groups, Annals of Mathematics Studies, Princeton University Press, 1996
[Rei] I. Reiner, Maximal orders, Academic Press 1975
[Sc-Stxxx] P. Schneider, U. Stuhler: The cohomology of p-adic symmetric spaces, Invent. math. 105, (1991), 47–122
[Sch] I. Schur: Über vertauschbare lineare Differentialausdrücke, Sitzungsber. der Berliner Math. Gesell. 4 (1905), 2–8
[Se-Wi] G.B. Segal, G. Wilson: Loop groups and equations of KdV type, Publ. Math. I.H.E.S. 61 (1985), 5–65
[Sesh] C.S. Seshadri: Fibrés vectoriels sur les courbes algébriques (redigée par J.M. Drezet). Asterisque 96, (1982)
[Shio] T. Shiota: Characterization of Jacobian varieties in terms of soliton equations, Inv. Math. 83 (1986), 333–382
[Stxxx] U. Stuhler: p-adic homogeneous spaces and moduli problems, Math. Zeitschrift 192, (1986), 491–540
[Pu-Vo] M. van der Put, H. Voskuil: Symmetric spaces associated to split algebraic groups over a local field, J. reine angew. Math. 433, (1992), 69–100.
[Va-Po-Ma] J.M. Vázquez, M. Porras, and F.J.P. Martin: The algebraic formalism of soliton equations over arbitrary base fields, preprint 1996, 1–34 (alggeom/9606009)
[Ver] J.-L. Verdier: Equations differentielles algébriques, Séminaire de l’École Normale Supérieure 1979–82, Birkhäuser (1983), 215–236
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Blum, A., Stuhler, U. (1997). Drinfeld modules and elliptic sheaves. In: Narasimhan, M.S. (eds) Vector Bundles on Curves — New Directions. Lecture Notes in Mathematics, vol 1649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094426
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