Class field theory : its centenary and prospect
著者
書誌事項
Class field theory : its centenary and prospect
（Advanced studies in pure mathematics, 30）
Mathematical Society of Japan, c2001
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注記
Includes bibliographies
"The Seventh MSJ International Research Institute of the Mathematical Society of Japan was held in Tokyo for ten days from June 3rd to 12th, 1998. The theme was 'Class Field Theory - its Centenary and Prospect', which is taken as thetitle of the book."-Pref.
内容説明・目次
内容説明
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.
目次
Memories of Professor Teiji Takagi by S. Iyanaga On Artin $L$-functions by M. R. Murty 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 by G. Frei Nonabelian local reciprocity maps by I. Fesenko Embedding problems with restricted ramifications and the class number of Hilbert class fields by A. Nomura The history of the theorem of Shafarevich in the theory of class formations by H. Koch A survey of $p$-extensions by M. Yamagishi Galois module structure of $p$-class formations by T. Nguyen Quang Do A Dieudonne theory for $p$-divisible groups by T. Zink Hilbert's 12th problem, complex multiplication and Shimura reciprocity by P. Stevenhagen Hecke module structure of quaternions by D. R. Kohel On classification of semisimple algebraic groups by I. Satake The $L$-group by B. Casselman Groupe des obstructions pour les deformations de representations Galoisiennes by R. Gillard Abelian varieties over $\mathbf{Q}(\sqrt{6})$ with good reduction everywhere by R. Schoof Hodge cycles and unramified class fields by H. Yanai Recent progress on the finiteness of torsion algebraic cycles by N. Otsubo Finiteness of a certain motivic cohomology group of varieties over local and global fields by K. Sato Iwasawa theory--Past and present by R. Greenberg Iwasawa invariants of $\mathbb{Z}_p$-extensions over an imaginary quadratic field by M. Ozaki On $p$-adic zeta functions and class groups of $\mathbb{Z}_p$-extensions of certain totally real fields by H. Taya Class numbers of imaginary quadratic fields by W. Kohnen On parities of relative class numbers of certain CM-extensions by R. Okazaki Some congruences for binomial coefficients by S. G. Hahn and D. H. Lee Stably free and not free rings of integers by J. Cougnard The capitulation problem for certain number fields by M. Ayadi, A. Azizi, and M. C. Ismaili On the capitulation problem by H. Suzuki Adele geometry of numbers by M. Morishita and T. Watanabe On Shafarevich-Tate sets by T. Ono Class field theory in characteristic $p$, its origin and development by P. Roquette.
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