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Developments in Mathematics

Galois Theory and Modular Forms

Editors: Hashimoto, Ki-ichiro, Miyake, Katsuya, Nakamura, Hiroaki (Eds.)

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eBook $209.00
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  • ISBN 978-1-4613-0249-0
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Hardcover $269.00
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  • ISBN 978-1-4020-7689-3
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Softcover $269.00
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About this book

This volume is an outgrowth of the research project "The Inverse Ga­ lois Problem and its Application to Number Theory" which was carried out in three academic years from 1999 to 2001 with the support of the Grant-in-Aid for Scientific Research (B) (1) No. 11440013. In September, 2001, an international conference "Galois Theory and Modular Forms" was held at Tokyo Metropolitan University after some preparatory work­ shops and symposia in previous years. The title of this book came from that of the conference, and the authors were participants of those meet­ All of the articles here were critically refereed by experts. Some of ings. these articles give well prepared surveys on branches of research areas, and many articles aim to bear the latest research results accompanied with carefully written expository introductions. When we started our re~earch project, we picked up three areas to investigate under the key word "Galois groups"; namely, "generic poly­ nomials" to be applied to number theory, "Galois coverings of algebraic curves" to study new type of representations of absolute Galois groups, and explicitly described "Shimura varieties" to understand well the Ga­ lois structures of some interesting polynomials including Brumer's sextic for the alternating group of degree 5. The topics of the articles in this volume are widely spread as a result. At a first glance, some readers may think this book somewhat unfocussed.

Table of contents (21 chapters)

  • The Arithmetic of Weierstrass Points on Modular Curves X 0 (p)

    Ahlgren, Scott

    Pages 3-12

  • Semistable Abelian Varieties with Small Division Fields

    Brumer, Armand (et al.)

    Pages 13-37

  • Q-curves with Rational j-invariants and Jacobian Surfaces of GL2-type

    Hashimoto, Ki-ichiro

    Pages 39-64

  • Points Defined over Cyclic Quartic Extensions on an Elliptic Curve and Generalized Kummer Surfaces

    Kuwata, Masato

    Pages 65-76

  • The Absolute Anabelian Geometry of Hyperbolic Curves

    Mochizuki, Shinichi

    Pages 77-122

Buy this book

eBook $209.00
price for USA
  • ISBN 978-1-4613-0249-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $269.00
price for USA
  • ISBN 978-1-4020-7689-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $269.00
price for USA
  • ISBN 978-1-4613-7960-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Galois Theory and Modular Forms
Editors
  • Ki-ichiro Hashimoto
  • Katsuya Miyake
  • Hiroaki Nakamura
Series Title
Developments in Mathematics
Series Volume
11
Copyright
2004
Publisher
Springer US
Copyright Holder
Kluwer Academic Publishers
eBook ISBN
978-1-4613-0249-0
DOI
10.1007/978-1-4613-0249-0
Hardcover ISBN
978-1-4020-7689-3
Softcover ISBN
978-1-4613-7960-7
Series ISSN
1389-2177
Edition Number
1
Number of Pages
XII, 394
Topics