Modular Curves as Shimura Variety

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


Modular varieties classifying abelian varieties with a level structure, given endomorphism subring and polarization, by making the level structure finer and finer, give rise to a tower of varieties. This tower has a strikingly big automorphism group, which can be described by an adele group of an algebraic group. Such a tower with a big adelic automorphism group is called a Shimura variety (of PEL type; see (PAF)) because Shimura was the first to realize that the symmetry given by well-described automorphisms is essential in studying arithmetic problems and automorphic forms defined over the variety (see (Sh4) and his earlier papers quoted there, including (Sh2)).


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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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