Advanced Studies in Pure Mathematics 2001; 631 pp; hardcover Volume: 30 ISBN10: 4931469116 ISBN13: 9784931469112 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 TheoryIts 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 postpublication. Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. Readership 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 localglobal 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 theoryPast 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 CMextensions
 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 ShafarevichTate sets
 P. Roquette  Class field theory in characteristic \(p\), its origin and development
