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Jean Alexandre Eugène Dieudonné (French: [ʒɑ̃ alɛksɑ̃dʁ øʒɛn djødɔne]; 1 July 1906 – 29 November 1992) was a French mathematician, notable for research in abstract algebra, algebraic geometry, and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendieck, and as a ...
The Éléments de géométrie algébrique (EGA; from French: "Elements of Algebraic Geometry") by Alexander Grothendieck (assisted by Jean Dieudonné) is a rigorous treatise on algebraic geometry that was published (in eight parts or fascicles) from 1960 through 1967 by the Institut des Hautes Études Scientifiques.
In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x 2 = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers).
Chapter XII Topology and topological algebra; Chapter XIII Integration; Chapter XIV Integration in locally compact groups; Chapter XV Normed algebras and spectral theory; Dieudonné, J. (1968), Éléments d'analyse. Tome II: Chapitres XII à XV, Cahiers Scientifiques, vol. XXXI, Paris: Gauthier-Villars, MR 0235946
Written with the assistance of Jean Dieudonné, this is Grothendieck's exposition of his reworking of the foundations of algebraic geometry. It has become the most important foundational work in modern algebraic geometry. The approach expounded in EGA, as these books are known, transformed the field and led to monumental advances.
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials ; the modern approach generalizes this in a few different aspects.
Yuri Manin (1937–2023) – algebraic geometry and diophantine geometry; Vladimir Arnold (1937–2010) – algebraic geometry; Ernest Vinberg (1937–2020) J. H. Conway (1937–2020) – sphere packing, recreational geometry; Robin Hartshorne (1938–) – geometry, algebraic geometry; Phillip Griffiths (1938–) – algebraic geometry ...
The rigorous deductive methods of geometry found in Euclid's Elements of Geometry were relearned, and further development of geometry in the styles of both Euclid (Euclidean geometry) and Khayyam (algebraic geometry) continued, resulting in an abundance of new theorems and concepts, many of them very profound and elegant.