# Claude Chevalley

Claude Chevalley ( born February 11, 1909 in Johannesburg, South Africa, † 28 June 1984 in Paris) was a French-American mathematician and a member of Bourbaki.

## Life

Chevalley was the son of a French diplomat who wrote the Concise Oxford French Dictionary with Chevalleys mother. He studied from 1926 to the Ecole Normale Superieure in Paris under Emile Picard ( completion 1929) and continued his studies 1931/2 by Emil Artin in Hamburg and then in Marburg with Helmut Hasse on. There he was led to the study of the class field theory, which he received his doctorate in Paris in 1933. In Germany he met the Japanese mathematician Shokichi Iyanaga know, and its connection to Japan led to a series of lectures in 1953 in Tokyo, which was published as a book (one of the listeners Goro Shimura contributed by improved proof of Chevalley 's Lemma for book publication in ). Another close friend of the time in Germany was the late lamented Jacques Herbrand. In 1934 he was one of the founders of the Bourbaki - circle. In 1938 he went to the Institute for Advanced Study in Princeton, and remained there during the war. 1949-1957 he was professor of mathematics at Columbia University in New York, but then returned to France, where he (later the University of Paris VII) in 1957 professor at the University of Paris. A chair at the Sorbonne was refused, initially being advanced that he was an American citizen, and even after he proved that he still had French citizenship, the campaign went against his calling.

Chevalley was politically active in various groups, so that in his collected works, a band with non-mathematical writings appeared, edited by his daughter. For example, it was around 1970 with Alexander Grothendieck and Pierre Samuel in the pacifist and environmental group Survivre et vivre.

## Work

Chevalley was a typical algebraists and wrote in a tight, dry style. After Armand Borel, the dry Bourbaki style is mainly due to him. He served in algebra, algebraic geometry and number theory fundamental contributions. For example, " algebraisierte " he the class field theory with the introduction of Adele and Idele bypassing all transcendental elements such as Dirichlet series, among others and gave the theory of spinors ( Clifford algebras ) which had already been investigated Elie Cartan in France, an algebraic form. He also studied algebraic groups and found finite simple groups of Lie - type ( " Chevalley groups") by the theory of Lie algebras, before defined over the real or complex numbers, brought in an abstract form, they also finite fields defined.

The set of Chevalley (or Chevalley -Warning, in addition Ewald Warning) from 1936 gives solution conditions for polynomial systems of equations in r variables over finite fields (where the polynomials have no constant term ) and the solution is safe for sufficiently large number of variables. He thereby proved a conjecture of Artin that finite fields have been completed quasi- algebraic.

In Seminaire Chevalley / Cartan in Paris 1955/1956 and in the Seminaire Chevalley 1956/57, 1957/58 the basics of schema theory were laid, newly -founded algebraic geometry with the Alexander Grothendieck.

The lemma of anger originates from Chevalley and was informed by him Max anger verbally.

In 1941 he was awarded the Cole Prize for Algebra from the American Mathematical Society. In 1958 he gave a plenary lecture at the International Congress of Mathematicians in Edinburgh (La théorie of groupes algébriques ).

Chevalley contributed greatly to the results of the German school of algebraic Emmy Noether, Emil Artin, Helmut Hasse, first to America and then to France (Nicolas Bourbaki ) to transfer and develop.

His doctoral include Leon Ehrenpreis and Gerhard Hochschild.

## Works

- Collected Works. Springer Verlag, 3 volumes, 1997-2004 (Pierre Cartier ( Eds.), the non-mathematical parts of his daughter, the philosopher Catherine Chevalley, edited ). Volume 1 Class field theory, Volume 2 Algebraic theory of spinors and Clifford algebras, Volume 3 Classification of groupes semi- simples algebriques: the classification semi -simple algebraic groups
- Theory of Lie Groups. 3 vols, Princeton University Press and Paris, Hermann 1946, 1951, 1955.
- Introduction to the Theory of Algebraic Functions of One Variable, American Mathematical Society 1951, 1979
- The algebraic theory of spinors. New York, Columbia University Press 1954
- Class field theory. In 1954. (Also Collected Works, Vol.1 )
- The construction and study of Certain important algebras. The Mathematical Society of Japan, 1955.
- Fundamental concepts of algebra. New York, Academic Press 1956
- Sur la théorie du corps de classes dans les corps finis et les corps locaux, Dissertation 1934
- L' arithmétique dans les algebres de matrices, Paris, Hermann 1936
- Fondements de la géometrie algébrique, Paris 1958
- Sur certains groupes simples, Tohoku Mathematical Journal, Volume 7, 1955, pp. 14-66.
- La théorie du corps de classes, Annals of Mathematics, Volume 41, 1940, pp. 394-418