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Class Field Theory - Its Centenary and Prospect
Edited by: Katsuya Miyake
A publication of the Mathematical Society of Japan.
Advanced Studies in Pure Mathematics
2001; 631 pp; hardcover
Volume: 30
ISBN-10: 4-931469-11-6
ISBN-13: 978-4-931469-11-2
Order Code: ASPM/30

This volume is a collection of articles contributed by the speakers at the Mathematical Society of Japan's Seventh International Research Institute entitled, "Class Field Theory-Its Centenary and Prospect", held in Tokyo in June 1998. Some of the articles are expository; they discuss important interesting aspects of class field theory and contain full references. Other articles are historical; they vividly explain how leading number theorists in Europe and Japan developed and exchanged their mathematical ideas.

Volumes in this series are freely available electronically 5 years post-publication.

Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS.


Graduate students and research mathematicians interested in number theory.

Table of Contents

  • S. Iyanaga -- Memories of Professor Teiji Takagi
  • M. R. Murty -- On Artin \(L\)-functions
  • G. Frei -- How Hasse was led to the theory of quadratic forms, the local-global principle, the theory of the norm residue symbol, the reciprocity laws, and to class field theory
  • I. Fesenko -- Nonabelian local reciprocity maps
  • A. Nomura -- Embedding problems with restricted ramifications and the class number of Hilbert class fields
  • H. Koch -- The history of the theorem of Shafarevich in the theory of class formations
  • M. Yamagishi -- A survey of \(p\)-extensions
  • T. Nguyen Quang Do -- Galois module structure of \(p\)-class formations
  • T. Zink -- A Dieudonné theory for \(p\)-divisible groups
  • P. Stevenhagen -- Hilbert's 12th problem, complex multiplication and Shimura reciprocity
  • D. R. Kohel -- Hecke module structure of quaternions
  • I. Satake -- On classification of semisimple algebraic groups
  • B. Casselman -- The \(L\)-group
  • R. Gillard -- Groupe des obstructions pour les déformations de représentations Galoisiennes
  • R. Schoof -- Abelian varieties over \(\mathbf{Q}(\sqrt{6})\) with good reduction everywhere
  • H. Yanai -- Hodge cycles and unramified class fields
  • N. Otsubo -- Recent progress on the finiteness of torsion algebraic cycles
  • K. Sato -- Finiteness of a certain motivic cohomology group of varieties over local and global fields
  • R. Greenberg -- Iwasawa theory--Past and present
  • M. Ozaki -- Iwasawa invariants of \(\mathbb{Z}_p\)-extensions over an imaginary quadratic field
  • H. Taya -- On \(p\)-adic zeta functions and class groups of \(\mathbb{Z}_p\)-extensions of certain totally real fields
  • W. Kohnen -- Class numbers of imaginary quadratic fields
  • R. Okazaki -- On parities of relative class numbers of certain CM-extensions
  • S. G. Hahn and D. H. Lee -- Some congruences for binomial coefficients
  • J. Cougnard -- Stably free and not free rings of integers
  • M. Ayadi, A. Azizi, and M. C. Ismaili -- The capitulation problem for certain number fields
  • H. Suzuki -- On the capitulation problem
  • M. Morishita and T. Watanabe -- Adele geometry of numbers
  • T. Ono -- On Shafarevich-Tate sets
  • P. Roquette -- Class field theory in characteristic \(p\), its origin and development
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