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- 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 represented by a scheme $Z$, and the induced morphism of schemes $Z rightarrow V$ is a surjective étale morphism.
encyclopediaofmath.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.
You’ll learn what algebraic expressions are, how to simplify algebraic expressions, and the different methods for using algebraic expressions. Look out for the algebraic expression worksheets, word problems and exam questions at the end.
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 ...
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.
An algebraic space over S is a presheaf. F: (Sch/S)opp fppf Sets. with the following properties. The presheaf F is a sheaf. The diagonal morphism F → F × F is representable. There exists a scheme U ∈ Ob((Sch/S)fppf) and a map hU → F which is surjective, and étale.
Definition 4.1.1. A vector space over F is a set V together with the operations of addition V × V → V and scalar multiplication F × V → V satisfying each of the following properties. Commutativity: u + v = v + u u + v = v + u. for all u, v ∈ V u, v ∈ V.
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