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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.
Algebraic Expressions. Here is everything you need to know about algebraic expressions for GCSE maths (Edexcel, AQA and OCR). You’ll learn what algebraic expressions are, how to simplify algebraic expressions, and the different methods for using algebraic expressions.
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.
Algebraic terms are individual letters, groups of letters, or groups of letters and numbers separated by addition or subtraction in algebraic expressions. For example, this is an algebraic expression with three algebraic terms. Term 1 \;\;\; 1 Term 2 \;\;\; 2 Term 3 3.
Introduction. Conventions. Separation axioms. Points of algebraic spaces. Quasi-compact spaces. Special coverings. Properties of Spaces defined by properties of schemes. Constructible sets. Dimension at a point. Dimension of local rings. Generic points. Reduced spaces. The schematic locus. Obtaining a scheme. Points on quasi-separated spaces.
Lemma 65.6.2. A scheme is an algebraic space. More precisely, given a scheme T ∈Ob((Sch/S)fppf) the representable functor hT is an algebraic space. Proof. The functor hT is a sheaf by our remarks in Section 65.2. The diagonal hT → hT ×hT =hT×T is representable because (Sch/S)fppf has fibre products.
