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Chevalley
Claude Chevalley (; 11 February 1909 – 28 June 1984) was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory and the theory of algebraic groups. He was a founding member of the Bourbaki group. Life His father, Abel Chevalley, was a French diplomat who, jointly with his wife Marguerite Chevalley née Sabatier, wrote ''The Concise Oxford French Dictionary''. Chevalley graduated from the École Normale Supérieure in 1929, where he studied under Émile Picard. He then spent time at the University of Hamburg, studying under Emil Artin and at the University of Marburg, studying under Helmut Hasse. In Germany, Chevalley discovered Japanese mathematics in the person of Shokichi Iyanaga. Chevalley was awarded a doctorate in 1933 from the University of Paris for a thesis on class field theory. When World War II broke out, Chevalley was at Princeton University. After reporting to the French Embassy, he s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chevalley Group
In mathematics, specifically in group theory, the phrase ''group of Lie type'' usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field. The phrase ''group of Lie type'' does not have a widely accepted precise definition, but the important collection of finite simple groups of Lie type does have a precise definition, and they make up most of the groups in the classification of finite simple groups. The name "groups of Lie type" is due to the close relationship with the (infinite) Lie groups, since a compact Lie group may be viewed as the rational points of a reductive linear algebraic group over the field of real numbers. and are standard references for groups of Lie type. Classical groups An initial approach to this question was the definition and detailed study of the so-called ''classical groups'' over finite and other fields by . These groups were studied by L. E. Dick ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chevalley–Warning Theorem
In number theory, the Chevalley–Warning theorem implies that certain polynomial equations in sufficiently many variables over a finite field have solutions. It was proved by and a slightly weaker form of the theorem, known as Chevalley's theorem, was proved by . Chevalley's theorem implied Artin's and Dickson's conjecture that finite fields are quasi-algebraically closed fields . Statement of the theorems Let \mathbb be a finite field and \_^r\subseteq\mathbb _1,\ldots,X_n/math> be a set of polynomials such that the number of variables satisfies :n>\sum_^r d_j where d_j is the total degree of f_j. The theorems are statements about the solutions of the following system of polynomial equations :f_j(x_1,\dots,x_n)=0\quad\text\, j=1,\ldots, r. * The ''Chevalley–Warning theorem'' states that the number of common solutions (a_1,\dots,a_n) \in \mathbb^n is divisible by the characteristic p of \mathbb. Or in other words, the cardinality of the vanishing set of \_^r is 0 m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicolas Bourbaki
Nicolas Bourbaki () is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure - PSL (ENS). Founded in 1934–1935, the Bourbaki group originally intended to prepare a new textbook in analysis. Over time the project became much more ambitious, growing into a large series of textbooks published under the Bourbaki name, meant to treat modern pure mathematics. The series is known collectively as the ''Éléments de mathématique'' (''Elements of Mathematics''), the group's central work. Topics treated in the series include set theory, abstract algebra, topology, analysis, Lie groups and Lie algebras. Bourbaki was founded in response to the effects of the First World War which caused the death of a generation of French mathematicians; as a result, young university instructors were forced to use dated texts. While teaching at the University of Strasbourg, Henri Cartan complained to his colleague André Weil of the inadequac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Groups
In mathematics, an algebraic group is an algebraic variety endowed with a group structure which is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Many groups of geometric transformations are algebraic groups; for example, orthogonal groups, general linear groups, projective groups, Euclidean groups, etc. Many matrix groups are also algebraic. Other algebraic groups occur naturally in algebraic geometry, such as elliptic curves and Jacobian varieties. An important class of algebraic groups is given by the affine algebraic groups, those whose underlying algebraic variety is an affine variety; they are exactly the algebraic subgroups of the general linear group, and are therefore also called ''linear algebraic groups''. Another class is formed by the abelian varieties, which are the algebraic groups whose underlying variety is a projective variety. Chevalley's structure theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Louis Auguste Sabatier
Louis Auguste Sabatier (; 22 October 1839 – 12 April 1901), French Protestant theologian, was born at Vallon-Pont-d'Arc, Ardèche and died in Strasbourg. He was educated at the Protestant theological faculty of Montauban as well as at the universities of Tübingen and Heidelberg. After holding the pastorate at Aubenas in Ardèche from 1864 to 1868, he was appointed professor of reformed dogmatics at the Protestant theological faculty of Strasbourg. His markedly French sympathies during the War of 1870 led to his expulsion from Strassburg in 1872. After five years' effort he succeeded in establishing a Protestant Faculty of Theology in Paris (today: Faculté de théologie protestante de Paris) along with Eugène Ménégoz, and became professor and then dean. In 1886, he became a teacher in the newly founded religious science department of the École des Hautes Etudes at the Sorbonne. His brother, Paul, was a noted theological historian. He is the father of two daughter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helmut Hasse
Helmut Hasse (; 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 class field theory and diophantine geometry (Hasse principle), and to local zeta functions. Life Hasse was born in Kassel, Province of Hesse-Nassau, the son of Judge Paul Reinhard Hasse, also written Haße (12 April 1868 – 1 June 1940, son of Friedrich Ernst Hasse and his wife Anna Von Reinhard) and his wife Margarethe Louise Adolphine Quentin (born 5 July 1872 in Milwaukee, daughter of retail toy merchant Adolph Quentin (b. May 1832, probably Berlin, Kingdom of Prussia) and Margarethe Wehr (b. about 1840, Prussia), then raised in Kassel). After serving in the Imperial German Navy in World War I, he studied at the University of Göttingen, and then at the University of Marburg under Kurt Hensel, writing a dissertation in 1921 containing the Hasse–Mi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chevalley Scheme
A Chevalley scheme in algebraic geometry was a precursor notion of scheme theory. Let ''X'' be a separated integral noetherian scheme, ''R'' its function field. If we denote by X' the set of subrings \mathcal O_x of ''R'', where ''x'' runs through ''X'' (when X=\mathrm(A), we denote X' by L(A)), X' verifies the following three properties * For each M\in X' , ''R'' is the field of fractions of ''M''. * There is a finite set of noetherian subrings A_i of ''R'' so that X'=\cup_i L(A_i) and that, for each pair of indices ''i,j'', the subring A_ of ''R'' generated by A_i \cup A_j is an A_i-algebra of finite type. * If M\subseteq N in X' are such that the maximal ideal of ''M'' is contained in that of ''N'', then ''M=N''. Originally, Chevalley Claude Chevalley (; 11 February 1909 – 28 June 1984) was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory and the theory of algebraic groups. He was a f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michel Broué
Michel Broué (born 28 October 1946) is a French mathematician. He holds a chair at Paris Diderot University. Broué has made contributions to algebraic geometry and representation theory. In 2012 he became a fellow of the American Mathematical Society. retrieved 2012-11-10. He is the son of French historian Pierre Broué and the father of French director and screenwriter Isabelle Broué and of French journalist and radio producer Caroline Broué
Caroline may refer to:
People
*Caroline (given name), a feminine given n ...
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Class Field Theory
In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. Hilbert is credited as one of pioneers of the notion of a class field. However, this notion was already familiar to Kronecker and it was actually Weber who coined the term before Hilbert's fundamental papers came out. The relevant ideas were developed in the period of several decades, giving rise to a set of conjectures by Hilbert that were subsequently proved by Takagi and Artin (with the help of Chebotarev's theorem). One of the major results is: given a number field ''F'', and writing ''K'' for the maximal abelian unramified extension of ''F'', the Galois group of ''K'' over ''F'' is canonically isomorphic to the ideal class group of ''F''. This statement was generalized to the so called Artin reciprocity law; in the idelic language, writing ''C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lê Dũng Tráng
Lê Dũng Tráng, (born 1947 in Saigon) is a Vietnamese- French mathematician. Life and work In the 1950s, Lê Dũng Tráng came to France, where he attended the Lycée Louis-le-Grand in Paris. He obtained a Ph.D. degree at the University of Paris in 1969 and 1971 under the supervision of Claude Chevalley and Pierre Deligne. From 1975 to 1999, he was professor at the University of Paris VII and research director of the CNRS. From 1983 to 1995 he was also a professor at the École Polytechnique. From 2002 to 2009 he headed the department of mathematics at the International Centre for Theoretical Physics (ICTP), in Trieste, Italy. He was a frequent guest scientist at Harvard University (with Phillip Griffiths) and Northeastern University (with Terence Gaffney and David B. Massey). He is particularly concerned with singularity theory in the complex domain ( Milnor fibrations, perverse sheaves). In 2000 he was involved in promoting scientific exchange between the United Stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oscar Goldman (mathematician)
Oscar Goldman (1925 – 17 December 1986, Bryn Mawr) was an American mathematician, who worked on algebra and its applications to number theory. Oscar Goldman received his Ph.D in 1948 under Claude Chevalley at Princeton University. He was chair of the Mathematics Department at Brandeis University from 1952 to 1960. As chair of the department his immediate successor was Maurice Auslander. In 1962, Goldman left Brandeis to become a professor and chair of the mathematics department at the University of Pennsylvania. Murray Gerstenhaber and Chung Tao Yang had persuaded Provost David R. Goddard to hire Goldman to help improve the quality of U. Penn's mathematics department to the level of the mathematics departments of the University of Chicago, Harvard University, and Princeton University. From 1963 to 1967, Goldman served as the chair of the mathematics department of U. Penn., hired several outstanding mathematicians including Richard Kadison and Eugenio Calabi, and regularly c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leon Ehrenpreis
Eliezer 'Leon' Ehrenpreis (May 22, 1930 – August 16, 2010, Brooklyn) was a mathematician at Temple University who proved the Malgrange–Ehrenpreis theorem, the fundamental theorem about differential operators with constant coefficients. He previously held tenured positions at Yeshiva University and at the Courant Institute at New York University. Early life and education Leon was born in New York City to a family of Jewish immigrants from Eastern Europe. He graduated from Stuyvesant High School and studied Mathematics as an undergraduate at City College of New York. Afterward, he enrolled as a doctoral student at Columbia University where he studied under mathematician Claude Chevalley, obtaining his PhD in 1953 at the age of 23. His doctoral thesis was entitled "Theory of Distributions in Locally Compact Spaces". Religion Ehrenpreis was also a Rabbi, having received his ordination from the renowned Rabbi Moshe Feinstein. He was the author of a work on the Chumash and other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
