- Algebra
- >
- Abstract algebra
- >
- Morphisms
- >
- Morphisms of schemes

- Fields of abstract algebra
- >
- Algebraic geometry
- >
- Scheme theory
- >
- Morphisms of schemes

- Fields of abstract algebra
- >
- Category theory
- >
- Morphisms
- >
- Morphisms of schemes

- Fields of geometry
- >
- Algebraic geometry
- >
- Scheme theory
- >
- Morphisms of schemes

- Functions and mappings
- >
- Category theory
- >
- Morphisms
- >
- Morphisms of schemes

- Mathematical analysis
- >
- Functions and mappings
- >
- Morphisms
- >
- Morphisms of schemes

- Mathematical objects
- >
- Functions and mappings
- >
- Morphisms
- >
- Morphisms of schemes

- Mathematical relations
- >
- Functions and mappings
- >
- Morphisms
- >
- Morphisms of schemes

- Mathematical structures
- >
- Category theory
- >
- Morphisms
- >
- Morphisms of schemes

Smooth morphism

In algebraic geometry, a morphism between schemes is said to be smooth if
* (i) it is locally of finite presentation
* (ii) it is flat, and
* (iii) for every geometric point the fiber is regular. (

Quasi-compact morphism

In algebraic geometry, a morphism between schemes is said to be quasi-compact if Y can be covered by open affine subschemes such that the pre-images are quasi-compact (as topological space). If f is q

Universal homeomorphism

In algebraic geometry, a universal homeomorphism is a morphism of schemes such that, for each morphism , the base change is a homeomorphism of topological spaces. A morphism of schemes is a universal

Rational function

In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coe

Fpqc morphism

In algebraic geometry, there are two slightly different definitions of an fpqc morphism, both variations of faithfully flat morphisms. Sometimes an fpqc morphism means one that is faithfully flat and

Étale morphism

In algebraic geometry, an étale morphism (French: [etal]) is a morphism of schemes that is formally étale and locally of finite presentation. This is an algebraic analogue of the notion of a local iso

Flat morphism

In mathematics, 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 every stalk is a flat map of ri

Isogeny

In mathematics, in particular, in algebraic 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

Proper morphism

In algebraic geometry, a proper morphism between schemes is an analog of a proper map between complex analytic spaces. Some authors call a proper variety over a field k a complete variety. For example

Closed immersion

In algebraic geometry, a closed immersion of schemes is a morphism of schemes that identifies Z as a closed subset of X such that locally, regular functions on Z can be extended to X. The latter condi

Radicial morphism

In algebraic geometry, a morphism of schemes f: X → Y is called radicial or universally injective, if, for every field K the induced map X(K) → Y(K) is injective. (EGA I, (3.5.4)) This is a generaliza

Regular embedding

In algebraic geometry, a closed immersion of schemes is a regular embedding of codimension r if each point x in X has an open affine neighborhood U in Y such that the ideal of is generated by a regula

Locally acyclic morphism

In algebraic geometry, a morphism of schemes is said to be locally acyclic if, roughly, any sheaf on S and its restriction to X through f have the same étale cohomology, locally. For example, a smooth

Sheaf of algebras

In algebraic geometry, a sheaf of algebras on a ringed space X is a sheaf of commutative rings on X that is also a sheaf of -modules. It is quasi-coherent if it is so as a module. When X is a scheme,

Formally étale morphism

In commutative algebra and algebraic geometry, a morphism is called formally étale if it has a lifting property that is analogous to being a local diffeomorphism.

Quasi-finite morphism

In algebraic geometry, a branch of mathematics, a morphism f : X → Y of schemes is quasi-finite if it is of finite type and satisfies any of the following equivalent conditions:
* Every point x of X

© 2023 Useful Links.