Class field theory : its centenary and prospect ; [proceedings of the seventh MSJ international research institute of the Mathematical Society of Japan, Tokyo, June 3rd - 12th, 1998

Memories Of Professor Teiji Takagi / Shokichi Iyanaga -- On Artin L-functions / Maruti Ram Murty -- How Hasse Was Led To The Theory Of Quadratic Froms, The Local-global Principle, The Theory Of The Norm Residue Symbol, The Reciprocity Laws, And To Class Field Theory / Günther Frei -- Nonabelian Local Reciprocity Maps / Ivan Fesenko -- Embedding Problems With Restricted Remifications And The Calss Number Of Hilbert Class Fields / Akito Nomura -- History Of The Theorem Of Shafarevich In The Theory Of Class Formations / Helmut Koch -- Survey Of P-extensions / Masakazu Yamagishi -- Galois Module Structure Of P-class Formations / Thong Nguyen Quang Do -- Dieudonné Theory For P-divisible Groups / Thomas Zink -- Hilbert's 12th Problem, Complex Multiplication And Shimura Reciprocity / Peter Stevenhagen -- Hecke Module Structure Of Quaternions / David R. Kohel -- On Classification Of Semisimple Algebraic Groups / Ichiro Satake -- L-group / Bill Casselman -- Groupe Des Obstructions Pour Les Déformations De Repreésentations Galoisiennes / Roland Gillard -- Abelian Varieties Over Q(6) With Good Reduction Everywhere / René Schoof -- Hodge Cycles And Unramified Class Fields / Hiromichi Yanai -- Recent Progress On The Finiteness Of Torsion Algebraic Cycles / Noriyuki Otsubo -- Finiteness Of A Certain Motivic Cohomology Group Of Varieties Over Local And Global Fields / Kanetomo Sato -- Iwasawa Theory-past And Present / Ralph Greenberg -- Iwasawa Invariants Of Zp-extensions Over An Imaginary Quadratic Field / Manaby Ozaki -- On P-adic Zeta Functions And Class Groups Of Zp-extensions Of Certain Totally Real Fields -- Hisao Taya -- Class Numbers Of Imaginary Quadratic Fields / Winfried Kohnen -- On Parties Of Relative Class Numbers Of Certain Cm-extensions / Ryotaro Okazaki -- Some Congruences For Binomial Coefficients / Sang Geun Hahn And Dong Hoon Lee -- Stably Free And Not Gree Rings Of Integers / Jean Cougnard -- Capitulation Problem For Certain Number Fields / Mohammed Ayadi, Abdelmalek Azizi And Moulay Chrif Ismili -- On The Capitulation Problem -- Hiroshi Suzuki -- Adele Geometry Of Numbers / Masanori Morishita And Takao Watanabe -- On Shafarevich-tate Sets / Takashi Ono -- Class Field Theory In Characteristic P, Its Origin And Development / Peter Roquette. Edited By Kastuya Miyake. This Volume Is A Collection Of Articles Contributed By The Speakers Of The Seventh Msj International Research Institute Of The Mathematical Society Of Japan, Held In Tokyo For Ten Days From June 3rd To 12th, 1998. The Theme Was Class Field Theory - Its Centenary And Prospect.--pref. Includes Bibliographical References. Front Cover ......Page 1 Title ......Page 2 Copyright ......Page 3 Preface ......Page 4 Acknowledgement ......Page 6 Program ......Page 8 CONTENTS ......Page 12 Shokichi IYANAGA - Memories of Professor Teiji Takagi ......Page 14 Maruti Ram MURTY - On Artin L-Functions ......Page 26 G?nther 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 ......Page 44 Ivan FESENKO - Nonabelian Local Reciprocity Maps ......Page 76 Akito NOMURA - Embedding Problems with restricted Ramifications and the Class Number of Hilbert Class Fields ......Page 92 Helmut KOCH - The History of the Theorem of Shafarevich in the Theory of Class Formations ......Page 100 Masakazu YAMAGISHI - A Survey of p-Extensions ......Page 120 Thong NGUYEN QUANG Do - Galois Module Stucture of p-Class Formations ......Page 136 Thomas ZINK - A Dieudonne Theory for p-Divisible Groups ......Page 152 Peter STEVENHAGEN - Hilbert's 12th Problem, Complex Multiplication and Shimura Reciprocity ......Page 174 David R. KOHEL - Hecke Module Structure of Quaternions ......Page 190 Ichiro SATAKE - On Classification of Semisimple Algebraic Groups ......Page 210 Bill CASSELMAN - The L-Group ......Page 230 Roland GILLARD - Groupe des Obstructions pour les Deformations de Representations Galoisiennes ......Page 272 Rene SCHOOF - Abelian Varieties over Q( sqrt{6}) with Good Reduction Everywhere ......Page 300 Hiromichi YANAl - Hodge Cycles and Unramified Class Fields ......Page 320 Noriyuki OTSUBO - Recent Progress on the Finiteness of Torsion Algebraic Cycles ......Page 326 Kanetomo SATO - Finiteness of a certain Motivic Cohomology Group of Varieties over Local and Global Fields ......Page 338 Ralph GREENBERG - Iwasawa Theory - Past and Present ......Page 348 Manabu OZAKI - Iwasawa Invariants of Z_p-Extensions over an Imaginary Quadratic Field ......Page 400 Hisao TAYA - On p-Adic Zeta Functions and Class Groups of Z_p-Extensions of certain Totally Real Fields ......Page 414 Winfried KOHNEN - Class Numbers of Imaginary Quadratic Fields ......Page 428 Ryotaro OKAZAKI - On Parities of Relative Class Numbers of certain CM-Extensions ......Page 432 Sang Geun HAHN and Dong Hoon LEE - Some Congruences for Binomial Coefficients ......Page 458 Jean COUGNARD - Stably Free and Not Free Rings of Integers ......Page 476 Mohammed AYADI, Abdelmalek AZIZI and Moulay CHRIF ISMAILI - The Capitulation Problem for certain Number Fields ......Page 480 Hiroshi SUZUKI - On the Capitulation Problem ......Page 496 Masanori MORISHITA and Takao WATANABE - Adele Geometry of N umbers ......Page 522 Takashi ONO - On Shafarevich-Tate Sets ......Page 550 Peter ROQUETTE - Class Field Theory in Characteristic p, its Origin and Development ......Page 562 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. It includes articles that discuss important interesting aspects of class field theory and contains full references.