Claude Chevalley

Claude Chevalley (French:

When World War II broke out, Chevalley was at Princeton University. After reporting to the French Embassy, he stayed in the U.S., first at Princeton and then (after 1947) at Columbia University. His American students included Leon Ehrenpreis and Gerhard Hochschild. During his time in the U.S., Chevalley became an American citizen and wrote a substantial part of his lifetime's output in English.

When Chevalley applied for a chair at the

Chevalley had artistic and political interests, and was a minor member of the French non-conformists of the 1930s. The following quote by the co-editor of Chevalley's collected works attests to these interests:

"Chevalley was a member of various avant-garde groups, both in politics and in the arts... Mathematics was the most important part of his life, but he did not draw any boundary between his mathematics and the rest of his life."^[2]

Work

In his PhD thesis, Chevalley made an important contribution to the technical development of class field theory, removing a use of L-functions and replacing it by an algebraic method. At that time use of group cohomology was implicit, cloaked by the language of central simple algebras. In the introduction to André Weil's Basic Number Theory, Weil attributed the book's adoption of that path to an unpublished manuscript by Chevalley.

Around 1950, Chevalley wrote a three-volume treatment of

Chevalley's accurate discussion of integrality conditions in the

"Chevalley's theorem" (also called the

In the 1950s, Chevalley led some Paris seminars of major importance: the Séminaire Cartan–Chevalley of the academic year 1955-6, with

• 1936. L'Arithmetique dans les Algèbres de Matrices. Hermann, Paris.[3]
• 1940. "La théorie du corps de classes," Annals of Mathematics 41: 394–418.
• 1946. Theory of Lie groups. Princeton University Press.^[4]
• 1951. "Théorie des groupes de Lie, tome II, Groupes algébriques", Hermann, Paris.
• 1951. Introduction to the theory of algebraic functions of one variable, A.M.S. Math. Surveys VI.^[5]
• 1954. The algebraic theory of spinors, Columbia Univ. Press;^[6] new edition, Springer-Verlag, 1997.
• 1953–1954. Class field theory, Nagoya University.
• 1955. "Théorie des groupes de Lie, tome III, Théorèmes généraux sur les algèbres de Lie", Hermann, Paris.
• 1955, "Sur certains groupes simples," Tôhoku Mathematical Journal 7: 14–66.
• 1955. The construction and study of certain important algebras, Publ. Math. Soc. Japan.^[7]
• 1956. Fundamental concepts of algebra, Acad. Press.^[8]
• 1956–1958. "Classification des groupes de Lie algébriques", Séminaire Chevalley, Secrétariat Math., 11 rue P. Curie, Paris; revised edition by P.Cartier, Springer-Verlag, 2005.
• 1958. Fondements de la géométrie algébrique, Secrétariat Math., 11 rue P. Curie, Paris.

See also

• Idèle
• Valuative criterion of properness
• Chevalley group
• Chevalley scheme
• Chevalley–Iwahori–Nagata theorem
• Beck–Chevalley condition
• Non-conformist movement
• Jordan–Chevalley decomposition

Notes