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Generalization of the schemes of algebraic geometry
- In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Michael Artin 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.
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 · An algebraic space is a sheaf of sets $F$ in the étale topology of schemes satisfying the condition of local representability (in the étale topology): There exists a scheme $U$ and a sheaf morphism $\tilde U \rightarrow F$ such that for any scheme $V$ and morphism $\tilde V \rightarrow F$ the fibred product $\tilde U \times_F \tilde V$ is ...
An algebraic expression is a set of terms with letters and numbers that are combined using addition (+), subtraction (-), multiplication ( ) and division (÷). An expression that contains two terms is called a binomial.
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?
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?
Algebraic Geometry. Differential Geometry. Introduction. As its name suggests, algebraic geometry deals with curves or surfaces (or more abstract generalisations of these) which can be viewed both as geometric objects and as solutions of algebraic (specifically, polynomial) equations.
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