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In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Michael Artin [1] for use in deformation theory. Intuitively, schemes are given by gluing together affine schemes using the Zariski topology, while algebraic spaces are given by gluing together affine schemes using the finer étale topology.
Oct 9, 2017 · Algebraic space. A generalization of the concepts of a scheme and an algebraic variety. This generalization is the result of certain constructions in algebraic geometry: Hilbert schemes, Picard schemes, moduli varieties, contractions, which are often not realizable in the category of schemes and require its extensions.
In mathematics, a space is a set (sometimes known as a universe) endowed with a structure defining the relationships among the elements of the set. A subspace is a subset of the parent space which retains the same structure.
May 27, 2020 · Wikipedia defines an algebraic space X X to be a sheaf on the big étale site (Sch/S)et (Sch / S) e t, such that: There is a surjective étale morphism hX → X h X → X. The diagonal morphism ΔX/S: X → X ×X Δ X / S: X → X × X is representable. What does the first condition actually mean?
Jul 23, 2012 · What is the difference between a "space" and an "algebraic structure"? For example, metric spaces and vector spaces are both spaces and algebraic structures. Is a group a space? Is a manifold a space or an algebraic structure, both or neither?
A lgebra is a subfield of mathematics pertaining to the manipulation of symbols and their governing rules. The following is a compilation of symbols from the different branches of algebra, which include basic algebra, number theory, linear algebra and abstract algebra.
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set together with operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms implied by "vector space ...
