Finite morphism information

In algebraic geometry, a finite morphism between two affine varieties X , Y {\displaystyle X,Y} is a dense regular map which induces isomorphic inclusion...

naturally the structure of a locally ringed space; a morphism between algebraic varieties is precisely a morphism of the underlying locally ringed spaces. If X...

Hausdorff. A closed immersion is proper. A morphism is finite if and only if it is proper and quasi-finite. A morphism f: X → Y of schemes is called universally...

a scheme will be a scheme over some fixed base scheme S and a morphism an S-morphism. Contents:  !$@ A B C D E F G H I J K L M N O P Q R S T U V W XYZ...

is: a morphism f: X → Y of schemes is of finite type if Y has a covering by affine open subschemes Vi = Spec Ai such that f−1(Vi) has a finite covering...

theory of schemes in algebraic geometry, a flat morphism f from a scheme X to a scheme Y is a morphism such that the induced map on every stalk is a flat...

{\displaystyle f} is called a finite morphism if A {\displaystyle A} is a finite R {\displaystyle R} -algebra. Being a finite algebra is a stronger condition...

complex spaces, states that a proper morphism can be factorized as a composition of a finite mapping and a proper morphism with connected fibers. Roughly speaking...

a code. Every elementary morphism is a code. For L a subset of B∗, a finite subset T of L is a test set for L if morphisms f and g on B∗ agree on L if...

Morphism of finite type, a morphism of schemes with underlying morphisms on affine opens given by algebras of finite type Scheme of finite type, a scheme...

functor, because an S-morphism X → Y induces an S-morphism XF → YF. For example, consider a ring A of characteristic p > 0 and a finitely presented algebra...

Stein factorization, any surjective projective morphism is a contraction morphism followed by a finite morphism. Examples include ruled surfaces and Mori fiber...

geometry, an unramified morphism is a morphism f : X → Y {\displaystyle f:X\to Y} of schemes such that (a) it is locally of finite presentation and (b) for...

Press. p. 21. ISBN 9780201407518. Finitely generated module Finitely generated field extension Artin–Tate lemma Finite algebra Morphism of finite type...

a geometric morphism X → Y is to give a functor u∗: Y → X that preserves finite limits and all small colimits. Thus geometric morphisms between topoi...

map S ↪ A {\displaystyle S\hookrightarrow A} induces a surjective finite morphism of affine varieties X → A k d {\displaystyle X\to \mathbb {A} _{k}^{d}}...

_{S}^{n}\to S} where g is étale. A morphism of finite type is étale if and only if it is smooth and quasi-finite. A smooth morphism is stable under base change...

property of universal morphisms, given any morphism h : X 1 → X 2 {\displaystyle h:X_{1}\to X_{2}} there exists a unique morphism g : A 1 → A 2 {\displaystyle...

geometry, an isogeny is a morphism of algebraic groups (also known as group varieties) that is surjective and has a finite kernel. If the groups are abelian...

algébrique Fiber product of schemes Flat morphism Smooth scheme Finite morphism Quasi-finite morphism Proper morphism Semistable elliptic curve Grothendieck's...

^{r}} is a finite morphism. Projections can be used to cut down the dimension in which a projective variety is embedded, up to finite morphisms. Start with...

category, and the morphisms, which relate two objects called the source and the target of the morphism. One often says that a morphism is an arrow that...

A morphism of varieties is finite if the inverse image of every point is finite and the morphism is proper. A morphism of varieties is birational if...