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Automorphic vector bundles on connected Shimura varieties

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Bibliography

  • Borovoi, M.: Langlands's conjecture concerning conjugation of Shimura varieties. Sel. Math. Sov.3, 3–39 (1983/84)

    Google Scholar 

  • Deligne, P.: Equations Différentielles à Points Singuliers Réguliers. (Lect. Notes Math., vol. 163) Berlin Heidelberg New York: Springer 1970

    Google Scholar 

  • Deligne, P.: Travaux de Shimura. Sém. Bourbaki, Fév. 1971, Exposé 389. Lect. Notes Math. vol. 244. Berlin Heidelberg New York: Springer 1971

    Google Scholar 

  • Deligne, P.: Variétiés de Shimura: interpretation modulaire, et techniques de construction de modéles canoniques. Proc. Symp. Pure Math., A.M.S.,33, part 2, 247–290 (1979)

    Google Scholar 

  • Deligne, P.: Hodge cycles on abelian varieties (Notes by J.S. Milne). In: Hodge Cycles, Motives, and Shimura Varieties (Lect. Notes Math., vol. 900, Berlin Heidelberg New York: Springer 1982a, pp. 9–100)

    Google Scholar 

  • Deligne, P.: Motifs et groupes de Taniyama. In: Hodge Cycles, Motives, and Shimura Varieties, (Lect. Notes Math., vol. 900) Berlin Heidelberg New York: Springer 1982b, pp. 261–279

    Google Scholar 

  • Deligne, P., Milne J.: Tanhakian categories. In: Hodge Cycles, Motives, and Shimura Varieties. (Lect. Notes Math., vol. 900) Berlin Heidelberg New York: Springer 1982, pp. 101–228

    Google Scholar 

  • Grothendieck, A.: Etude locale des schémes et des morphismes de schémas Inst. Hautes Etudes Sci., Publ. Math.32, 5–361 (1967)

    Google Scholar 

  • Harris, M.: Arithmetic vector bundles on Shimura varieties. In: (Satake I., Morita, Y. (ed).) Automorphic Forms of Several Variables Prog. Math. 46, Birkhäuser, Boston, 1984, pp. 138–159

    Google Scholar 

  • Harris, M.: Arithmetic vector bundles and automorphic forms on Shimura varieties. I. Invent. math.82, 151–189 (1985)

    Google Scholar 

  • Hartshorne, R.: Ample Subvarieties of Algebraic Varieties. Lect. Notes Math., vol. 156) Berlin Heidelberg New York: Springer 1970

    Google Scholar 

  • Helgason, S.: Differential Geometry, Lie Groups, and Symmetric Spaces. New York: Academic Press, 1978

    Google Scholar 

  • Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry I, II, New York: Wiley (Interscience) 1963/69

    Google Scholar 

  • Langlands, R.: Automorphic representations Shimura varieties, and motives. Ein Märchen. Proc. Symp. Pure Math., A.M.S.,33, 205–246 (1979)

    Google Scholar 

  • Milne, J.: Etale Cohomology, Princeton: Princeton University Press 1980

    Google Scholar 

  • Milne, J.: The action of an automorphism of ℂ on a Shimura variety and its special points. Prog. Math. Vol. 35, Boston: Birkhäuser, 1983, pp. 239–265

    Google Scholar 

  • Milne, J.: Arithmetic Duality Theorems, Perspectives in Math., 1, Boston: Academic Press 1986

    Google Scholar 

  • Milne, J., Shih, K.-y.: Langlands's construction of the Taniyama group. In: Hodge Cycles, Motives, and Shimura Varieties (Lect. Notes Math., vol. 900, Berlin Heidelberg New York: Springer 1982a, pp. 229–260

    Google Scholar 

  • Milne, J., Shih, K.-y.: Conjugates of Shimura varieties.In: Hodge Cycles, Motives, and Shimura Varieties (Lect. Notes Math., vol. 900, Berlin Heidelberg New York: Springer 1982b, pp. 280–356

    Google Scholar 

  • Mumford, D.: Geometric Invariant Theory. Berlin Heidelberg New York: Springer 1965

    Google Scholar 

  • Murakami, S.: Cohomology Groups of Vector-valued Forms on Symmetric Spaces, mimeographed notes, University of Chicago, 1966

  • Platonov, V., Rapincuk, A.: On the group of rational points of three-dimensional groups. Sov. Math. Dokl.20, 693–697 (1979)

    Google Scholar 

  • Saavedra Rivano, N.: Catégories Tannakiennes. (Lect. Notes Math., vol. 265) Berlin Heidelberg New York: Springer 1972

    Google Scholar 

  • Shimura, G.: On some problems of algebraicity. Proc. Int. Cong. Math. 1978, Vol I, pp. 373–379

    Google Scholar 

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Parts of this work have supported by the National Science Foundation; it was completed while the author was at the sematical Sciences Research Institute, Berkeley

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Milne, J.S. Automorphic vector bundles on connected Shimura varieties. Invent Math 92, 91–128 (1988). https://doi.org/10.1007/BF01393994

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