Galois Theory and Modular Forms
Editors: Hashimoto, Ki-ichiro, Miyake, Katsuya, Nakamura, Hiroaki (Eds.)
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- About this book
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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)
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The Arithmetic of Weierstrass Points on Modular Curves X 0 (p)
Pages 3-12
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Semistable Abelian Varieties with Small Division Fields
Pages 13-37
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Q-curves with Rational j-invariants and Jacobian Surfaces of GL2-type
Pages 39-64
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Points Defined over Cyclic Quartic Extensions on an Elliptic Curve and Generalized Kummer Surfaces
Pages 65-76
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The Absolute Anabelian Geometry of Hyperbolic Curves
Pages 77-122
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Table of contents (21 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Galois Theory and Modular Forms
- Editors
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- 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
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