In algebraic 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...

of étale morphism (and so étale cohomology) depends on the flat morphism concept: an étale morphism being flat, of finite type, and unramified. Consider...

contains a uniformizer of K {\displaystyle K} . Abhyankar's lemma Unramified morphism Cassels, J.W.S. (1986). Local Fields. London Mathematical Society...

diagonal morphism is a closed immersion. Also, a morphism p : X → S {\displaystyle p:X\to S} locally of finite presentation is an unramified morphism if and...

notion of unramified morphism in algebraic geometry. It serves to define étale morphisms. Let f : X → Y {\displaystyle f:X\to Y} be a morphism of schemes...

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

morphism is unramified if it is unramified at every point in X {\displaystyle X} . One example of a morphism which is flat and generically unramified...

_{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...

{\displaystyle {\mathcal {O}}_{Y,y}} . The morphism f {\displaystyle f} is unramified (resp. G-unramified) if it is locally of finite type (resp. locally...

Frobenius is the augmentation map OS/Ip → OS/I. X is unramified over S if and only if FX/S is unramified and if and only if FX/S is a monomorphism. X is étale...

is unramified at x. Finite morphisms are quasi-finite. A quasi-finite proper morphism locally of finite presentation is finite. Indeed, a morphism is...

the closed immersion determined by J, and every Y-morphism g : Z0 → X, there exists a unique Y-morphism s : Z → X such that g = si. It is equivalent to...

as an étale morphism in general (under some slightly stronger hypotheses, on flatness and separability). Generically, then, such a morphism resembles a...

ring is called unramified if the corresponding morphism is unramified. 2.  An ideal in a polynomial ring over a field is called unramified for some extension...

to various algebro-geometric notions. A morphism f : X → Y {\displaystyle f:X\to Y} of schemes is unramified if and only if Ω X / Y {\displaystyle \Omega...

{\mathcal {O}}_{L}} . In fact, unramified morphisms of schemes in algebraic geometry are a direct generalization of unramified extensions of number fields...

extension of k containing all p-power roots of unity and A(p) is the maximal unramified abelian p-extension of k ^ ( C ) {\displaystyle {\hat {k}}(C)} . The description...

Proposition—Given a morphism f : X → Y {\displaystyle f:X\to Y} of finite type between Noetherian schemes, f {\displaystyle f} is étale (flat and unramified) if and...

{\displaystyle f} has no branch points, it is called unbranched. See also unramified morphism. Ahlfors, Lars (1979), Complex analysis (3rd ed.), McGraw Hill, ISBN 0-07-000657-1...

making an abelian variety from a morphism of algebraic curves. In its original form, it was applied to an unramified double covering of a Riemann surface...

smooth morphism vanishes. Furthermore, when any of the functors which extended the sequence of Kähler differentials were applied to a smooth morphism, they...

geometric point of view, L corresponds to another curve C′, together with a morphism π : C′ → C. Geometrically, the assertion that π is ramified at a finite...

theory of adeles. A morphism of schemes f : Y → X {\displaystyle f:Y\to X} is called a Nisnevich morphism if it is an étale morphism such that for every...

{\displaystyle G} -covers with n {\displaystyle n} branch points is an unramified cover of the configuration space Conf n {\displaystyle \operatorname {Conf}...

subject. One special casepg 93 of such an extension is taking the maximal unramified extension K u r / K {\displaystyle K^{ur}/K} and considering the ring...

"Functoriality Principle". Given two reductive groups and a (well behaved) morphism between their corresponding L-groups, this conjecture relates their automorphic...

lifting v, then A is said to be 0-unramified (or 0-neat). A is said to be 0-étale if it is 0-smooth and 0-unramified. The notion of 0-smoothness is also...

a cover of the branch point itself. Such covers are therefore always unramified. 0 is a branch point of the square root function. Suppose w = z1/2, and...

k_{x}=1} for an x ∈ X {\displaystyle x\in X} , then x {\displaystyle x} is unramified. The image point y = f ( x ) ∈ Y {\displaystyle y=f(x)\in Y} of a ramification...

(ii) A is a Nagata domain ⇒ {\displaystyle \Rightarrow } A analytically unramified ⇒ {\displaystyle \Rightarrow } the integral closure of the completion...