Iwasawa Kenkichi

Iwasawa Kenkichi ( Japanese 岩 澤 健 吉 ; born September 11, 1917 in Shinshuku, Kiryū ; † October 26, 1998 in Tokyo ) was a Japanese mathematician who made fundamental contributions to algebraic number theory , especially the theory of the field of circles . He also dealt with topological groups and Lie groups .

Life

Iwasawa went to the Musashi High School in Tokyo - the forerunner of today's Musashi University - and studied at the Imperial University of Tokyo from 1937 . He graduated in 1940, became an assistant and received his doctorate in 1945. During the war years he fell ill with pleurisy and was only able to return to the university in 1947, where he was assistant professor from 1949 to 1955. In 1950 he traveled to the United States , where he gave an Invited Lecture at the ICM in Cambridge (Massachusetts) in 1950 ( A note on L functions ). From 1950 to 1952 he was at the Institute for Advanced Study in Princeton (New Jersey) , then until 1967 professor at MIT in Cambridge (Massachusetts) and then until his retirement in 1986 professor at Princeton. In 1987 he returned to Tokyo with his wife.

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Iwasawa is best known for his work on algebraic number theory, especially the creation of the deep- seated Iwasawa theory of the extensions of algebraic number fields , in which, for example, in the theory of the field of circular division he not only uses the fields of the p th roots of unity over the rational numbers (with p odd prime number), but at the same time also the infinite tower of the circular dividing bodies formed from the adjunction -th roots of unity. ${\displaystyle p^{n}}$

The starting point was his attempt to understand Ernst Eduard Kummer's criterion for characterizing irregular prime numbers (which divide the class number of the field of the p -th roots of unity over the rational numbers) and the p -adic zeta functions of Kubota and Leopoldt. About the connection between the analytical and algebraic aspects of his theory, he made the Iwasawa conjectures , which were later proven by Barry Mazur and Andrew Wiles .

In addition to his work on number theory, his work on the theory of topological groups and Lie groups made him known. He did important work (Annals of Mathematics 1949) to solve the 5th Hilbert problem (which asks whether every locally Euclidean topological group is a Lie group ), a very active research area at the time. In this context he introduced the Iwasawa decomposition in 1949 ( On some types of topological groups , Annals of Mathematics).

In Japan he received the Asahi Prize in 1959 , the Japanese Academy Prize in 1962, and the Fujiwara Prize in 1979. In 1962 he received the Cole Prize . In 1970 he was invited speaker at the International Congress of Mathematicians in Nice ( On some infinite abelian extensions of algebraic number fields ) and in 1962 in Stockholm ( A class number formula for cyclotomic fields ). In 1955 he was elected to the American Academy of Arts and Sciences .

His students included Ralph Greenberg and Lawrence C. Washington .

literature

• Washington: Introduction to cyclotomic fields , Springer, Graduate Texts in Mathematics, 1998 ISBN 0387947620
• Serge Lang : Cyclotomic fields , Springer, Graduate Texts in Mathematics, 1978 ISBN 0387903070
• Iwasawa: Lectures on p-adic L-Functions , Princeton 1972
• Iwasawa: Local class field theory , 1986 ISBN 0195040309
• Iwasawa: Algebraic functions ; translated by Goro Kato, 1993 ISBN 0821845950
• Iwasawa: Kenkichi Iwasawa collected papers ; edited by Ichiro Satake et al. , 2001 ISBN 4431703144
• Iwasawa: On some types of topological groups , Ann. of Math., Vol. 50, 1949, pp. 507-558
• Iwasawa: On solvable extensions of algebraic number fields , Ann. of Math (2), Vol. 58, 1953, pp. 548-572
• Iwasawa: On the rings of valuation vectors , Ann. of Math. (2), Vol. 57, 1953, pp. 332-356
• Iwasawa: On-extensions of algebraic number fields , Bulletin of the American Mathematical Society, Volume 65, 1959, pp. 183-226

Web links

• Obituary by John Coates, Notices AMS 1999
• Memories from Ralph Greenberg
• Ralph Greenberg Iwasawa Theory - Past and Present , Advanced Studies in Pure Math. Vol. 30, 2001, pp.335-385 as Postscript file
• Interview with Iwasawa 1993

Japanese name: As is common in Japan, the family name comes before the first name in this article . So Iwasawa is the family name, Kenkichi the first name.