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Geometry of Variety

  • Haruzo Hida
Chapter
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

In this short chapter, we summarize geometric properties of a variety and a tower of varieties we need in the book. One reason for adding this chapter is to make the book logically complete, and another is to give the foundation of the theory of towers of varieties in the language of proschemes, since the Shimura variety is a tower of varieties fundamental to the number-theoretic study of automorphic forms. If the reader is familiar with the subject, he or she can take a brief look at the content of this chapter and go directly to Chap.6.

Keywords

Projective System Automorphic Form Projective Limit Closed Scheme Coherent Sheaf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [BCM]
    N. Bourbaki, Algèbre Commutative (Hermann, Paris, 1961–1998)Google Scholar
  2. [CRT]
    H. Matsumura, Commutative Ring Theory. Cambridge Studies in Advanced Mathematics, vol. 8 (Cambridge University Press, New York, 1986)Google Scholar
  3. [EGA]
    A. Grothendieck, J. Dieudonné, Eléments de Géométrie Algébrique. Publications IHES, vol. 4 (1960), vol. 8 (1961), vol. 11 (1961), vol. 17 (1963), vol. 20 (1964), vol. 24 (1965), vol. 28 (1966), vol. 32 (1967)Google Scholar
  4. [TCF]
    M. Nagata, Theory of Commutative Fields (American Mathematical Society, Providence, RI, 1993)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Haruzo Hida
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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