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On arithmetic varieties II

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Abstract

An arithmetic variety is the quotient space of a symmetric space with complex structure by an arithmetic subgroup of the associated algebraic Lie group. It is shown that the variety obtained from an arithmetic variety by a base change corresponding to any automorphism ofC is again an arithmetic variety.

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References

  1. W. L. Baily and A. Borel,Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math.84 (3), (1966), 442–528.

    Article  MathSciNet  Google Scholar 

  2. M. Borovoy,Shimura-Deligne schemes M c (G, h) and rational cohomology (Cp·p)—classes for abelian varieties, inGroup Theory and Homological Algebra, Vol. I, Jaroslavel, 1977.

  3. P. Deligne,Variétés de Shimura, in Proc. Sympos. Pure Math., Vol. 33, Amer. Math. Soc., Providence, R.I., 1979.

    Google Scholar 

  4. R. Hartshorne,Stable reflexive sheaves, Math. Ann.254 (2), (1980), 121–176.

    Article  MATH  MathSciNet  Google Scholar 

  5. D. Kazhdan,On arithmetic varieties, inLie Groups and their Representations (I. M. Gelfand, ed.), Akadémiai Kiadó, Budapest, 1975.

    Google Scholar 

  6. S. Kobayashi,Hyperbolic Manifolds and Holomorphic Mappings, Dekker, New York, 1970.

    MATH  Google Scholar 

  7. A. Koranyi and J. Wolf,Generalized Cayley transform of bounded symmetric domains, Am. J. Math.87 (1965), 899–939.

    Article  MATH  MathSciNet  Google Scholar 

  8. G. Margulis, Lecture at International Congress of Mathematicians, Vancouver, 1974.

  9. D. Montgomery and L. Zippin,Topological Transformation Groups, Interscience Publ., New York, 1955.

    MATH  Google Scholar 

  10. D. Mumford,Algebraic Geometry I, Complex Projective Varieties, Springer Verlag, 1976.

  11. J. Piatetskii-Shapiro,Automorphic Functions and the Geometry of Classical Domains, Gordon and Breach, New York, 1969.

    Google Scholar 

  12. J.-P. Serre,Geometrie Algebrique et Geometrie Analytique, Vol. VI, Annales Inst. Fourier, Grenoble, 1956.

    Google Scholar 

  13. Y. T. Siu,Extending coherent analytic sheaves, Ann. of Math.90 (1969), 108–143.

    Article  MathSciNet  Google Scholar 

  14. Y. T. Siu,Extension of meromorphic maps into Kähler manifolds, Ann. of Math.102 (1975), 421–462.

    Article  MathSciNet  Google Scholar 

  15. J. Tits,Classification of algebraic semisimple groups, in Proc. Sympos. Pure Math., Vol. 9, Amer. Math. Soc., Providence, R.I., 1966.

    Google Scholar 

  16. S. T. Yau,Calabi's conjecture and some new results in algebraic geometry, Proc. Natl. Acad. Sci. U.S.A.74 (1977), 1798–1799.

    Article  MATH  Google Scholar 

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Research partially supported by NSF Grant # MCS-77-15524.

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Kazhdan, D. On arithmetic varieties II. Israel J. Math. 44, 139–159 (1983). https://doi.org/10.1007/BF02760617

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  • DOI: https://doi.org/10.1007/BF02760617

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