affine scheme
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Affine — may refer to:*Affine cipher, a special case of the more general substitution cipher *Affine combination, a certain kind of constrained linear combination *Affine connection, a connection on the tangent bundle of a differentiable manifold *Affine… … Wikipedia
Scheme (mathematics) — In mathematics, a scheme is an important concept connecting the fields of algebraic geometry, commutative algebra and number theory. Schemes were introduced by Alexander Grothendieck so as to broaden the notion of algebraic variety; some consider … Wikipedia
Affine Grassmannian — In mathematics, the term affine Grassmannian has two distinct meanings. In one meaning the affine Grassmannian (manifold) is the manifold of all k dimensional subspaces of a finite dimensional vector space, while (described here) the affine… … Wikipedia
Glossary of scheme theory — This is a glossary of scheme theory. For an introduction to the theory of schemes in algebraic geometry, see affine scheme, projective space, sheaf and scheme. The concern here is to list the fundamental technical definitions and properties of… … Wikipedia
Function field (scheme theory) — In algebraic geometry, the function field KX of a scheme X is a generalization of the notion of a sheaf of rational functions on a variety. In the case of varieties, such a sheaf associates to each open set U the ring of all rational functions on … Wikipedia
Normal scheme — In mathematics, in the field of algebraic geometry, a normal scheme is a scheme X for which every stalk (local ring) OX,x of its structure sheaf OX is an integrally closed local ring; that is, each stalk is an integral domain such that its… … Wikipedia
Group scheme — In mathematics, a group scheme is a group object in the category of schemes. That is, it is a scheme G with the equivalent properties* there is a group law expressible as a multiplication μ and inversion map ι on G ; or * G is a functor (as in… … Wikipedia
Proj construction — In algebraic geometry, Proj is a construction analogous to the spectrum of a ring construction of affine schemes, which produces objects with the typical properties of projective spaces and projective varieties. It is a fundamental tool in scheme … Wikipedia
Grothendieck topology — In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space. A category together with a choice of Grothendieck topology is called a … Wikipedia
Algebraic space — In mathematics, an algebraic space is a generalization of the schemes of algebraic geometry introduced by Michael Artin for use in deformation theory.DefinitionAn algebraic space X comprises a schemeOne can always assume that U is an affine… … Wikipedia
Finite morphism — In algebraic geometry, a branch of mathematics, a morphism of schemes is a finite morphism, if Y has an open cover by affine schemes Vi = SpecBi such that for each i, f − 1(Vi) = Ui is an open affine subscheme SpecAi, and the restriction of … Wikipedia
