affine morphism

См. также в других словарях:

• 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

• Proper morphism — In algebraic geometry, a proper morphism between schemes is an analogue of a proper map between topological spaces. Contents 1 Definition 2 Examples 3 Properties and characterizations of proper morphisms …   Wikipedia

• Étale morphism — In algebraic geometry, a field of mathematics, an étale morphism (pronunciation IPA|) is an algebraic analogue of the notion of a local isomorphism in the complex analytic topology. They satisfy the hypotheses of the implicit function theorem,… …   Wikipedia

• Dévissage — In algebraic geometry, dévissage is a technique introduced by Alexander Grothendieck for proving statements about coherent sheaves on noetherian schemes. Dévissage is an adaptation of a certain kind of noetherian induction. It has many… …   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

• 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

• Blowing up — This article is about the mathematical concept of blowing up. For information about the physical/chemical process, see Explosion. For other uses of Blow up , see Blow up (disambiguation). Blowup of the affine plane. In mathematics, blowing up or… …   Wikipedia

• Field of definition — In mathematics, the field of definition of an algebraic variety V is essentially the smallest field to which the coefficients of the polynomials defining V can belong. Given polynomials, with coefficients in a field K , it may not be obvious… …   Wikipedia

• Flat topology — In mathematics, the flat topology is a Grothendieck topology used in algebraic geometry. It is used to define the theory of flat cohomology; it also has played a fundamental role in the theory of descent (faithfully flat descent). [… …   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

• Coherent sheaf — In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a specific class of sheaves having particularly manageable properties closely linked to the geometrical properties of the underlying space …   Wikipedia