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Teiji Takagi one of the leading number theorists of this century, is most renowned as the founder of class field theory. This volume reflects the stages of his development of this theory. Inspired by a genial idea related to analytic number theory, he developed a beautiful general theory of abelian extensions of algebraic number fields which he addressed at the ICM 1920 at Strasbourg. This report ends with a problem to generalize the results to the case of normal, not necessarily abelian extensions. Up to now this problem has stimulated research. This second edition incorporates the whole contents of "The Collected Papers of Teiji Takagi" edited by S. Kuroda, published by Iwanami Shoten in 1974. Following additions have been made: Note on Eulerian squares (1946).- Concept of numbers.- K. Iwasawa: On arithmetical papers of Takagi.- K. Yosida: On analytical papers of Takagi.- S. Iyanaga: On life and works of Takagi.
A propos de l'auteur
Kunihiko Kodaira was born on March 16, 1915 in Tokyo, Japan. He graduated twice from the University of Tokyo, with a degree in mathematics in 1938 and one in physics in 1941. From 1944 until 1949, Kodaira was an associate professor at the University of Tokyo but by this time his work was well known to mathematicians worldwide and in 1949 he accepted an invitation from H. Weyl to come to the Institute for Advanced Study. During his 12 years in Princeton, he was also Professor at Princeton University from 1952 to 1961. After a year at Harvard, he was then appointed in 1962 to the chair of mathematics at Johns Hopkins University, which heleft in 1965 for a chair at Stanford University. Finally, after 2 years at Stanford, he returned to Japan to Tokyo University from 1967. He died in Kofu, Japan, in 1997.Kodaira s work covers many topics, including applications of Hilbert space methods to differential equations, harmonic integrals , and importantly the application of sheaves to algebraic geometry. Around 1960 he became involved in the classification of compact complex analytic spaces. One of the themes running through much of his work is the "Riemann-Roch theorem" and this played an important role in much of his research. Kodaira received many honours for his outstanding research, in particular the "Fields Medal", in 1954.
