Morphism of schemes information

category of schemes. A morphism of algebraic stacks generalizes a morphism of schemes. By definition, a morphism of schemes is just a morphism of locally...

A morphism is finite if and only if it is proper and quasi-finite. A morphism f: X → Y of schemes is called universally closed if for every scheme Z with...

in particular in the 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...

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

omitted; i.e., 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...

morphism may refer to: Graph homomorphism, in graph theory, a homomorphism between graphs Graph morphism, in algebraic geometry, a type of morphism of...

finite map (in view of the previous definition, because it is between affine varieties). A morphism f: X → Y of schemes is a finite morphism if Y has an open...

rough idea of a morphism of schemes X → Y as a family of schemes parametrized by Y. Let X, Y, and Z be schemes over a field k, with morphisms X → Y and Z...

If X is an S-scheme and the Frobenius morphism of S is the identity, then the absolute Frobenius morphism is a morphism of S-schemes. In general, however...

case of the fact that a faithfully flat quasi-compact morphism of schemes has this property.). See also Flat morphism § Properties of flat morphisms. A...

In algebraic geometry, given a morphism f: X → S of schemes, the cotangent sheaf on X is the sheaf of O X {\displaystyle {\mathcal {O}}_{X}} -modules Ω...

algebraic geometry, a morphism f : X → S {\displaystyle f:X\to S} between schemes is said to be smooth if (i) it is locally of finite presentation (ii)...

classes each determined by a morphism f: X → Ω, the characteristic morphism of that class, which we take to be the subobject of X characterized or named by...

Affine scheme, the spectrum of prime ideals of a commutative ring Affine morphism, a morphism of schemes such that the pre-image of an open affine subscheme...

the relative dimension of a morphism of schemes is also important. By definition, the dimension of a scheme X is the dimension of the underlying topological...

a smooth scheme over k is locally of finite type. There is a more general notion of a smooth morphism of schemes, which is roughly a morphism with smooth...

difference between organisms of distinct populations in a species Muller's morphs, a classification scheme for genetic mutations "-morph", a suffix commonly used...

Algebra of finite type, an associative algebra with finitely many generators Morphism of finite type, a morphism of schemes with underlying morphisms on affine...

sending an affine morphism f : Y → X {\displaystyle f:Y\to X} to f ∗ O Y . {\displaystyle f_{*}{\mathcal {O}}_{Y}.} A morphism of schemes f : X → Y {\displaystyle...

a closed immersion of schemes is a morphism of schemes f : Z → X {\displaystyle f:Z\to X} that identifies Z as a closed subset of X such that locally...

slightly different definitions of an fpqc morphism, both variations of faithfully flat morphisms. Sometimes an fpqc morphism means one that is faithfully...

over a scheme S and if i is an S-morphism, then i is a regular embedding. In particular, every section of a smooth morphism is a regular embedding. If Spec...

be a morphism of schemes. The morphism f induces several functors. Specifically, it gives adjoint functors f* and f* between the categories of sheaves...