Information om | Engelska ordet GROTHENDIECK

Exempel på hur man kan använda GROTHENDIECK i en mening

• In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C that makes the objects of C act like the open sets of a topological space.
• In the 1950s and 1960s, a fruitful collaboration between Serre and the two-years-younger Alexander Grothendieck led to important foundational work, much of it motivated by the Weil conjectures.
• The Weil conjectures about zeta functions of varieties over finite fields, proved by Dwork, Grothendieck, Deligne and others.
• The assumption of the existence of a strongly inaccessible cardinal is sometimes applied in the form of the assumption that one can work inside a Grothendieck universe, the two ideas being intimately connected.
• The question of points was close to resolution by 1950; Alexander Grothendieck took a sweeping step (invoking the Yoneda lemma) that disposed of it—naturally at a cost, that every variety or more general scheme should become a functor.
• As a first step in generalizing Serre duality, Grothendieck showed that this version works for schemes with mild singularities, Cohen–Macaulay schemes, not just smooth schemes.
• After 1945 he started his own seminar in Paris, which deeply influenced Jean-Pierre Serre, Armand Borel, Alexander Grothendieck and Frank Adams, amongst others of the leading lights of the younger generation.
• Scheme theory was introduced by Alexander Grothendieck in 1960 in his treatise Éléments de géométrie algébrique (EGA); one of its aims was developing the formalism needed to solve deep problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne).
• The approach of Alexander Grothendieck is concerned with the category-theoretic properties that characterise the categories of finite G-sets for a fixed profinite group G.
• This theory initially appeared as an extension of the ideas of distribution theory; it was soon connected to the local cohomology theory of Grothendieck, for which it was an independent realisation in terms of sheaf theory.
• In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjectures.
• Although fifty-seven is not prime, it is jokingly known as the Grothendieck prime after a legend according to which the mathematician Alexander Grothendieck supposedly gave it as an example of a particular prime number.
• In algebraic geometry, motives (or sometimes motifs, following French usage) is a theory proposed by Alexander Grothendieck in the 1960s to unify the vast array of similarly behaved cohomology theories such as singular cohomology, de Rham cohomology, etale cohomology, and crystalline cohomology.
• The Éléments de géométrie algébrique ("Elements of Algebraic Geometry") by Alexander Grothendieck (assisted by Jean Dieudonné), or EGA for short, is a rigorous treatise, in French, on algebraic geometry that was published (in eight parts or fascicles) from 1960 through 1967 by the Institut des Hautes Études Scientifiques.
• In particular, he authored the book Cohomologie non-abélienne (Springer, 1971) and proved the theorem that bears his name, which gives a characterization of a Grothendieck topos.
• On the other hand, the direct image of a coherent sheaf under a proper morphism is coherent, by results of Grauert and Grothendieck.
• This had been shown by Grothendieck if the morphism f: X → Y is locally of finite presentation, which follows from the other assumptions if Y is noetherian.
• Originally, they were introduced by Alexander Grothendieck to keep track of automorphisms on moduli spaces, a technique which allows for treating these moduli spaces as if their underlying schemes or algebraic spaces are smooth.
• I: Mon→Grp is the functor sending every monoid to the submonoid of invertible elements and K: Mon→Grp the functor sending every monoid to the Grothendieck group of that monoid.
• Back in Zürich for 1968 and 1969 he proposed elementary (first-order) axioms for toposes generalizing the concept of the Grothendieck topos (see History of topos theory) and worked with the algebraic topologist Myles Tierney to clarify and apply this theory.

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