On arithmetic varieties II
Tóm tắt
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.
Tài liệu tham khảo
W. L. Baily and A. Borel,Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math.84 (3), (1966), 442–528.
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.
P. Deligne,Variétés de Shimura, in Proc. Sympos. Pure Math., Vol. 33, Amer. Math. Soc., Providence, R.I., 1979.
R. Hartshorne,Stable reflexive sheaves, Math. Ann.254 (2), (1980), 121–176.
D. Kazhdan,On arithmetic varieties, inLie Groups and their Representations (I. M. Gelfand, ed.), Akadémiai Kiadó, Budapest, 1975.
S. Kobayashi,Hyperbolic Manifolds and Holomorphic Mappings, Dekker, New York, 1970.
A. Koranyi and J. Wolf,Generalized Cayley transform of bounded symmetric domains, Am. J. Math.87 (1965), 899–939.
G. Margulis, Lecture at International Congress of Mathematicians, Vancouver, 1974.
D. Montgomery and L. Zippin,Topological Transformation Groups, Interscience Publ., New York, 1955.
D. Mumford,Algebraic Geometry I, Complex Projective Varieties, Springer Verlag, 1976.
J. Piatetskii-Shapiro,Automorphic Functions and the Geometry of Classical Domains, Gordon and Breach, New York, 1969.
J.-P. Serre,Geometrie Algebrique et Geometrie Analytique, Vol. VI, Annales Inst. Fourier, Grenoble, 1956.
Y. T. Siu,Extending coherent analytic sheaves, Ann. of Math.90 (1969), 108–143.
Y. T. Siu,Extension of meromorphic maps into Kähler manifolds, Ann. of Math.102 (1975), 421–462.
J. Tits,Classification of algebraic semisimple groups, in Proc. Sympos. Pure Math., Vol. 9, Amer. Math. Soc., Providence, R.I., 1966.
S. T. Yau,Calabi's conjecture and some new results in algebraic geometry, Proc. Natl. Acad. Sci. U.S.A.74 (1977), 1798–1799.