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Generalization of the schemes of algebraic geometry
- Algebraic space In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Michael Artin for use in deformation theory.
en.wikipedia.org/wiki/Algebraic_space
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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.
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?
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?
Abstract algebra is a broad field of mathematics, concerned with algebraic structures such as groups, rings, vector spaces, and algebras. On the 12-hour clock, 9+4=1 9+4=1, rather than 13 as in usual arithmetic.
Apr 23, 2012 · You may consider a topological space, with a structure of open sets (fulfilling certain properties) - like a plane with open balls, its sums and so on. You may consider an algebraic object, like vector space, with algebraic structure, given by, for example, addition.
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