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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.
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
In mathematics, a Dieudonné module introduced by Jean Dieudonné (1954, 1957b), is a module over the non-commutative Dieudonné ring, which is generated over the ring of Witt vectors by two special endomorphisms and called the Frobenius and Verschiebung operators. They are used for studying finite flat commutative group schemes.
SGA6 Théorie des intersections et théorème de Riemann-Roch, 1966–1967 (Intersection theory and the Riemann–Roch theorem), Lecture Notes in Mathematics 225, 1971; SGA7 Groupes de monodromie en géométrie algébrique, 1967–1969 (Monodromy groups in algebraic geometry), Lecture Notes in Mathematics 288 and 340, 1972/3. SGA8 was never ...
Alexander Grothendieck, later Alexandre Grothendieck in French (/ ˈ ɡ r oʊ t ən d iː k /; German: [ˌalɛˈksandɐ ˈɡʁoːtn̩ˌdiːk] ⓘ; French: [ɡʁɔtɛndik]; 28 March 1928 – 13 November 2014), was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry.
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).
In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry. (See Areas of mathematics and Algebraic geometry.)