Concept
Alexander Grothendieck
Related concepts (56)
Projective tensor product
In functional analysis, an area of mathematics, the projective tensor product of two locally convex topological vector spaces is a natural topological vector space structure on their tensor product. Namely, given locally convex topological vector spaces and , the projective topology, or π-topology, on is the strongest topology which makes a locally convex topological vector space such that the canonical map (from to ) is continuous. When equipped with this topology, is denoted and called the projective tensor product of and .
Injective tensor product
In mathematics, the injective tensor product of two topological vector spaces (TVSs) was introduced by Alexander Grothendieck and was used by him to define nuclear spaces. An injective tensor product is in general not necessarily complete, so its completion is called the . Injective tensor products have applications outside of nuclear spaces.
Overcategory
In mathematics, specifically , an overcategory (and undercategory) is a distinguished class of used in multiple contexts, such as with covering spaces (espace etale). They were introduced as a mechanism for keeping track of data surrounding a fixed object in some category . There is a dual notion of undercategory, which is defined similarly. Let be a category and a fixed object of pg 59. The overcategory (also called a slice category) is an associated category whose objects are pairs where is a morphism in .
Hilbert scheme
In algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The basic theory of Hilbert schemes was developed by . Hironaka's example shows that non-projective varieties need not have Hilbert schemes.
Roger Godement
Roger Godement (ɡɔdmɑ̃; 1 October 1921 – 21 July 2016) was a French mathematician, known for his work in functional analysis as well as his expository books. Godement started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major results; this work was in parallel but independent of similar investigations in the USSR and Japan.
Étale fundamental group
The étale or algebraic fundamental group is an analogue in algebraic geometry, for schemes, of the usual fundamental group of topological spaces. In algebraic topology, the fundamental group of a pointed topological space is defined as the group of homotopy classes of loops based at . This definition works well for spaces such as real and complex manifolds, but gives undesirable results for an algebraic variety with the Zariski topology.