Claude Chevalley (11 February 1909 - 28 June 1984) was a French mathematician who made important contributions to number theory, algebraic geometry and the theory of algebraic groups. He was born in Johannesburg, and died in Paris. He was a founding member of the Bourbaki group. February 11 is the 42nd day of the year in the Gregorian Calendar. ... Year 1909 (MCMIX) was a common year starting on Friday (see link for calendar). ... June 28 is the 179th day of the year (180th in leap years) in the Gregorian Calendar, with 186 days remaining. ... 1984 (MCMLXXXIV) was a leap year starting on Sunday of the Gregorian calendar. ... Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ... In algebraic geometry, an algebraic group is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety. ... City motto: Unity in Development Province Gauteng Mayor Amos Masondo Area  - % water 1,644 km² 0. ... City flag City coat of arms Motto: Fluctuat nec mergitur (Latin: Tossed by the waves, she does not sink) Paris Eiffel tower as seen from the esplanade du Trocadéro. ... Nicolas Bourbaki is the collective allonym under which a group of mainly French 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. ...

After graduating from the École Normale Supérieure, he studied under Emil Artin in Hamburg from 1931, a time which may have formed his mathematical taste, and where he had contact with the Japanese school in the person of Shokichi Iyanaga, and then under Helmut Hasse. One of his achievements was a step in 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 his book Basic Number Theory, Chevalley's friend André Weil explains that the book's adoption of that road goes back to an old, unpublished manuscript of Chevalley. The quadrangle at the main ENS building on rue dUlm is known as the Cour aux Ernests – the Ernests being the goldfish in the pond. ... Emil Artin (March 3, 1898-December 20, 1962) was an Austrian mathematician born in Vienna who spent his career in Germany (mainly in Hamburg) until the Nazi threat when he emigrated to the USA in 1937 where he was at Indiana University 1938-1946, and Princeton University 1946-1958. ... Helmut Hasse (pronounced HAHS uh) (25 August 1898- 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local classfield theory and diophantine geometry (Hasse principle), and to local zeta functions. ... In mathematics, class field theory is a major branch of algebraic number theory. ... The theory of L-functions has become a very substantial, and still largely conjectural, part of contemporary number theory. ... In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well as in applications to group theory proper, group cohomology is a way to study groups using a sequence of functors H n. ... In ring theory and related areas of mathematics a central simple algebra (CSA) over K, also called a Brauer algebra after Richard Brauer, is a finite-dimensional (associative) algebra A, which is a simple ring, and for which the center is exactly K. For example, the complex numbers C form... André Weil (May 6, 1906 - August 6, 1998) was one of the great mathematicians of the 20th century. ...

Chevalley also wrote a three-volume treatment of Lie groups around 1950. A few years later he published an investigation into what are now called Chevalley groups, and for which he is most remembered. An accurate discussion of conditions of integrality in the Lie algebras of semisimple groups enabled their theory to be abstracted from the real and complex fields. As a consequence, analogues over finite fields could be defined. This was an essential stage in the theory of the finite simple groups. After Chevalley's work the distinction between 'classical groups' falling into the Dynkin diagram classification, and 'sporadic groups' which did not, became sharp enough to be useful. What are called 'twisted' groups of the classical families could be fitted into the picture. In mathematics, a Lie group is a group whose elements can be continuously parametrized by real numbers, such as the rotation group, which can be parametrized by the Euler angles. ... In mathematics, a group of Lie type is a finite group related to the points of a simple algebraic group with values in a finite field. ... In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. ... In abstract algebra, a finite field or Galois field (so named in honor of Évariste Galois) is a field that contains only finitely many elements. ... In mathematics, a simple group is a group which is not the trivial group and whose only normal subgroups are the trivial group and the group itself. ... See also Simple Lie group. ... The classification of the finite simple groups is a vast body of work in mathematics, mostly published between around 1955 and 1983, which is thought to classify all of the finite simple groups. ...

Chevalley's theorem usually refers to his result on solubility of equations over a finite field (also called the Chevalley-Warning theorem). Another theorem concerns the "constructible" sets in algebraic geometry, i.e. those in the Boolean algebra generated by the Zariski-open and closed sets. It states that the image of such a set by a morphism of algebraic varieties is of the same type. In logicians' terms, this is an 'elimination of quantifiers'. In mathematics, Chevalleys theorem on solutions of polynomial equations over a finite field F with q elements, q a power of the prime number p, states that for a polynomial P(X1, ..., XN) of total degree d, with d < N, the number M of solutions of P(X1, ..., XN... Quantifier elimination is a technique in logic, model theory, and theoretical computer science. ...

Chevalley in the 1950s led some Paris seminars (working groups) of major importance: the Séminaire Cartan-Chevalley of the academic year 1955/6, with Henri Cartan, and the Séminaire Chevalley of 1956/7 and 1957/8. These dealt with topics on algebraic groups and the foundations of algebraic geometry, as well as pure algebra. This was the actual point of genesis of scheme theory, in the Cartan-Chevalley seminar; though the subsequent development by Alexander Grothendieck was so rapid, thorough and inclusive that its historical tracks can appear well covered. The more specialised ideas of Serre, Chevalley, Shimura and probably others such as Kähler and Nagata were all subsumed. Henri Cartan (born July 8, 1904) is a son of Élie Cartan, and is, as his father was, a distinguished and influential French mathematician. ... In algebraic geometry, an algebraic group is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ... In mathematics, a scheme is an important concept connecting the fields of algebraic geometry, commutative algebra and number theory. ... Alexander Grothendieck (Berlin, March 28, 1928) is one of the most important mathematicians of the 20th century. ...

In 1939 he was at Princeton University. After reporting to the French Embassy at the outbreak of World War II, he stayed in the USA, taking a position in 1947 at Columbia University, and becoming an American citizen. Subsequently, when he wanted to return to France, his difficulties in a candidature for a Sorbonne chair were described by André Weil in a polemical piece (Science Française?, in La Nouvelle N. R. F. — Chevalley was the professeur B of the piece, as confirmed in the endnote to the reprint in Weil, Oeuvres Scientifiques, tome II). He later (1957) did obtain a position at the Université de Paris VII. He had a number of distinguished students. [1] Princeton University is a coeducational private university located in Princeton, New Jersey, in the United States of America. ... Combatants Allied powers: China France Great Britain Soviet Union United States and others Axis powers: Germany Italy Japan and others Commanders Chiang Kai-shek Charles de Gaulle Winston Churchill Joseph Stalin Franklin Roosevelt Adolf Hitler Benito Mussolini Hideki Tōjō Casualties Military dead: 17,000,000 Civilian dead: 33,000... Columbia University is a private research university in the United States. ... The Sorbonne, Paris, in a 17th century engraving The historic University of Paris (French: ) first appeared in the second half of the 12th century, but was in 1970 reorganised as 13 autonomous universities (University of Paris I–XIII). ... André Weil (May 6, 1906 - August 6, 1998) was one of the great mathematicians of the 20th century. ... The University of Paris VII: Denis Diderot is a university in Paris, France. ...

Chevalley's works have been published in six volumes, edited by Pierre Cartier and Catherine Chevalley. Pierre Cartier (born in Sedan, France in 1932) is a mathematician. ...

Incidentally, Chevalley discovered Zorn's Lemma before Max Zorn did himself and mentioned it to Zorn as a way to simplify a proof in one of the latter's papers. However, like many mathematical results, this lemma has been attributed to the wrong person. Zorns lemma, also known as the Kuratowski-Zorn lemma, is a proposition of set theory that states: Every non-empty partially ordered set in which every chain (i. ... Max August Zorn (June 6, 1906 in Krefeld, Germany - March 9, 1993 in Bloomington, Indiana, USA) was a German-born American mathematician. ...

Selected bibliography

• Theory of Lie groups, I, Princeton, Princeton University Press, 1946.
• Sur certaines groupes simples, Tôhoku Mathematical Journal 7 (1955), 14 – 66.

See also

• idèle
• valuative criterion of properness
• Chevalley group
• Chevalley scheme
• Beck-Chevalley condition

In mathematics, an adelic algebraic group is a topological group defined by an algebraic group G over a number field K, and the adele ring A = A(K) of K. It consists of the points of G having values in A; the definition of the appropriate topology is straightforward only... In mathematics, a continuous function between topological spaces is called proper if inverse images of compact subsets are compact. ... In mathematics, a group of Lie type is a finite group related to the points of a simple algebraic group with values in a finite field. ... A Chevalley scheme in algebraic geometry was a precursor notion of scheme theory. ...

External links

• O'Connor, John J., and Edmund F. Robertson. "Claude Chevalley". MacTutor History of Mathematics archive.
• Claude Chevalley in the Mathematics Genealogy Project