Claude Chevalley

from Wikipedia, the free encyclopedia

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

Chevalley (center) with Yazuo Akizuki (left), Akira Kobori (right)

Life

Chevalley was the son of the French diplomat Abel Chevalley , who wrote the Concise Oxford French Dictionary with Chevalley's mother, Marguerite Chevalley (1880-1979), née Sabatier and daughter of the French Reformed theologian Louis Auguste Sabatier . From 1926 he studied at the Ecole Normale Superieure in Paris under Émile Picard (graduated in 1929) and continued his studies in 1931/2 with Emil Artin in Hamburg and then in Marburg with Helmut Hasse . There he was led to occupation with the class field theory, on which he received his doctorate in Paris in 1933. In Germany he also met the Japanese mathematician Shokichi Iyanaga , and his connection to Japan led to a series of lectures in Tokyo in 1953, which was also published as a book (one of the listeners Gorō Shimura also carried an improved proof of Chevalley's lemma to the book publication at). Another close friend from his time in Germany was Jacques Herbrand, who died early . In 1934 he became one of the founding fathers of the Bourbaki group . In 1938 he went to the Institute for Advanced Study at Princeton and stayed there during the war. 1949–1957 he was professor of mathematics at Columbia University in New York, but then returned to France, where he was professor at the University of Paris (later the University of Paris VII) in 1957. He was denied a professorship at the Sorbonne, initially pretending that he was an American citizen, and even after proving that he still had French citizenship, the campaign against his appeal continued.

Chevalley was politically active in various groups and was interested in philosophy, so that in his collected works a volume with non-mathematical writings appeared, edited by his daughter. For example, around 1970 he was with Alexander Grothendieck and Pierre Samuel in the pacifist and environmental group Survivre et vivre . In the 1930s he was close to the nonconformist movement of the Ordre Nouveau by Arnaud Dandier . Philosophically he was close to Émile Meyerson .

In 1965 he became a corresponding member of the Académie des sciences .

plant

Chevalley was a typical algebraist and wrote in a short, dry style. According to Armand Borel , the dry Bourbaki style is mainly due to him. He made fundamental contributions to algebra, algebraic geometry and number theory . For example, he "algebraized" the class field theory with the introduction of the Adele and Idele , bypassing all transcendent elements such as Dirichlet series and the like. a. and gave the theory of spinors ( Clifford algebras ), which Élie Cartan had already studied in France, an algebraic form. He also investigated algebraic groups and found finite simple groups of the Lie type (" Chevalley groups ") by bringing the theory of Lie algebras , previously defined using real or complex numbers, into an abstract form that it also uses finite bodies. The Chevalley-Eilenberg complex for the construction of a cohomology for a Lie algebra representation is associated with its name.

The Chevalley theorem (or Chevalley-Warning, additionally after Ewald Warning) from 1936 gives solution conditions for polynomial systems of equations in variables over finite fields (whereby the polynomials do not have a constant term) and ensures the solution for a sufficiently large number of variables. He thus proved a conjecture by Artin that finite fields are quasi-algebraically closed.

In Seminaire Chevalley / Cartan in Paris 1955/1956 and Seminaire Chevalley 1956/57, 1957/58 the basics of were scheme set theory, with Alexander Grothendieck to algebraic geometry newly established.

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

Chevalley contributed significantly to transferring and developing the results of the German algebraic school around Emmy Noether , Emil Artin , and Helmut Hasse, first to America and then to France ( Nicolas Bourbaki ).

His doctoral students include Leon Ehrenpreis and Gerhard Hochschild .

Fonts

  • About the theory of corps de classes in the corps finis et les corps locaux. In: Imperial University of Tokyo. Journal of the Faculty of Science. Section 1: Mathematics, Astronomy, Physics, Chemistry. Volume 2, No. 9, 1933, pp. 365-476, (dissertation 1934; digitized version ).
  • L'arithmétique dans les algèbres de matrices (= Actualités Scientifiques et Industrielles. 323, ISSN  0365-6861 = Actualités Scientifiques et Industrielles. Exposés Mathématiques. 14). Hermann, Paris 1936.
  • The theory of corps de classes. In: Annals of Mathematics . Series 2, Volume 41, No. 2, 1940, pp. 394-418, doi : 10.2307 / 1969013 .
  • Theory of Lie Groups. / Théorie des groupes de Lie. 3 volumes. 1946, 1951, 1955;
    • Theory of Lie Groups. I (= Princeton Mathematical Series. 8, ISSN  0079-5194 ). Princeton University Press, Princeton NJ 1946;
    • Théorie des groupes de Lie. Volume 2: Groupes algébriques (= Actualités Scientifiques et Industrielles. 1152 = Publications de l'Institut de Mathématique de l'Université de Nancago. 1). Hermann, Paris 1951;
    • Théorie des groupes de Lie. Volume 3: Théorèmes généraux sur les algèbres de Lie (= Actualités Scientifiques et Industrielles. 1226 = Publications de l'Institut de Mathématique de l'Université de Nancago. 4). Hermann, Paris 1954.
  • Introduction to the Theory of Algebraic Functions of One Variable (= Mathematical Surveys. 6, ISSN  0076-5376 ). American Mathematical Society, New York NY et al. 1951.
  • Class field theory. Nagoya University, Nagoya 1953-1954.
  • The algebraic theory of spinors. Columbia University Press, New York NY 1954.
  • The construction and study of certain important algebras (= Publications of the Mathematical Society of Japan. 1, ISSN  0549-4540 ). The Mathematical Society of Japan, Tokyo 1955.
  • Sur certains groupes simples. In: Tôhoku Mathematical Journal. Volume 7, No. 1/2, 1955, pp. 14-66, doi : 10.2748 / tmj / 1178245104 .
  • Fundamental concepts of algebra (= Pure and Applied Mathematics. 7, ISSN  0079-8169 ). Academic Press, New York NY 1956.
  • Fondements de la geometry algébrique. Mathématiques approfondies 1957/1958. Secrétariat Mathématique, Faculté des Sciences de Paris, Paris 1958.
  • Collected Works. 2 volumes. Editors: Pierre Cartier , Catherine Chevalley Springer, Berlin et al. 1997–
    • Volume 2: The algebraic theory of spinors and Clifford algebras. 1997, ISBN 3-540-57063-2 ;
    • Volume 3: Classification des groupes algébriques semi-simples. 2005, ISBN 3-540-23031-9 .

literature

Web links

Individual evidence

  1. ↑ Chevalley's friend André Weil plays it in Science Française? In: La Nouvelle Revue Française . 3 ° année, no. 25, January 1, 1955, pp. 97-109, with Professor A on p. 102 is meant Carl Ludwig Siegel , with Professor B Chevalley. The difficulties of Chevalley in France are contrasted with the case of Siegel, who was received with open arms in Göttingen. On-line
  2. ↑ Giorgio Bolondi: Bourbaki. In: Claudio Bartocci, Renato Betti, Angelo Guerraggio, Roberto Lucchetti (Eds.): Mathematical Lives. Protagonists of the Twentieth Century From Hilbert to Wiles. Springer, Berlin et al. 2011, ISBN 978-3-642-13605-4 , pp. 123–130, here p. 129.
  3. ^ List of members since 1666: Letter C. Académie des sciences, accessed on October 29, 2019 (French).
  4. ↑ Pierre Cartier recalls that while Chevalley avoided all diagrams in lectures, he still drew a diagram on the blackboard on one occasion when he was trying to clarify a difficult point. However, he carefully hid the whole thing from his students by shielding the drawing with his body and quickly erasing it. Siobhan Roberts: King of Infinite Space. Donald Coxeter, the Man who Saved Geometry. Walker & Company, New York NY 2006, ISBN 0-8027-1499-4 , p. 158.
  5. ^ Chevalley: Demonstration d'une hypothèse de M. Artin. In: Treatises from the Mathematical Seminar of the University of Hamburg . Volume 11, 1935, pp. 73–75, doi : 10.1007 / BF02940714 , Warning's essay comment on the above work is in the same volume, pp. 76–83, doi : 10.1007 / BF02940715 .
  6. ↑ The sum of the degrees of the individual polynomials must be less than the number of variables.
  7. ^ For Chevalley: La théorie du corps de classes. In: Annals of Mathematics. Volume 41, No. 2, 1940, pp. 394-418.
  8. ↑ Volume 1 did not appear.
  9. ↑ The non-mathematical parts were edited by his daughter, the philosopher Catherine Chevalley.
personal data
SURNAME Chevalley, Claude
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH February 11, 1909
PLACE OF BIRTH Johannesburg
DATE OF DEATH June 28, 1984
Place of death Paris