analytically unramified ring is a local ring whose completion is reduced (has no nonzero nilpotent). The following rings are analytically unramified:...

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

an ideal appears in a theorem of Rees that characterizes an analytically unramified ring. In C [ x , y ] {\displaystyle \mathbb {C} [x,y]} , x i y d −...

spectra of rings S p e c O K → S p e c O L {\displaystyle \mathrm {Spec} {\mathcal {O}}_{K}\to \mathrm {Spec} {\mathcal {O}}_{L}} . In fact, unramified morphisms...

is unramified outside a finite set S of primes of K (i.e. if there is a finite set S of primes of K such that any prime of K not in S is unramified in...

  A local ring is called analytically unramified if its completion has no nonzero nilpotent elements. 3.  A local ring is called analytically irreducible...

extension is unramified if, and only if, the discriminant is the unit ideal. The Minkowski bound above shows that there are no non-trivial unramified extensions...

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, except...

properties: f {\displaystyle f} is flat and unramified. f {\displaystyle f} is a smooth morphism and unramified. f {\displaystyle f} is flat, locally of...

Riemann surface cannot be analytically continued to a cover of the branch point itself. Such covers are therefore always unramified. 0 is a branch point of...

notions. A morphism f : X → Y {\displaystyle f:X\to Y} of schemes is unramified if and only if Ω X / Y {\displaystyle \Omega _{X/Y}} is zero. A special...

field, G is an unramified group defined over F, in other words a quasi-split reductive group defined over F that splits over an unramified extension of...

Galois group G, and C a union of conjugacy classes of G, the number of unramified primes of K of norm below x with Frobenius conjugacy class in C is | C...

are modules over the p-adic completion of the maximal unramified extension of Zp, a much larger ring containing nth roots of unity for all n not divisible...

schemes, f {\displaystyle f} is étale (flat and unramified) if and only if for each x in X, f is an analytically local isomorphism near x; i.e., with y = f...

maximal order in Q(τ) is the ring of algebraic integers of Q(τ), and values of τ having it as its associated order lead to unramified extensions of Q(τ). These...

results is: given a number field F, and writing K for the maximal abelian unramified extension of F, the Galois group of K over F is canonically isomorphic...

called Oka pseudoconvex. Oka's proof of Levi's problem was that when the unramified Riemann domain over C n {\displaystyle \mathbb {C} ^{n}} was a domain...

straightforward to prove that a simple algebra over a local field has an unramified splitting field than to prove the corresponding statement for 2-cohomology...

K} 's ring of integers, there is an Euler factor, which is easiest to define in the case where p {\displaystyle {\mathfrak {p}}} is unramified in L {\displaystyle...

{\displaystyle G_{p}} ( p < ∞ ) {\displaystyle (p<\infty )} is called unramified, if the vector space V π p K p = { v ∈ V π p ∣ π p ( k ) v = v ∀ k ∈ K...

ramifiés de variétés algébriques, d'après S. Lang (class field theory for unramified coverings of algebraic varieties) René Thom, Les singularités des applications...

of semisimple Lie algebras and groups 1960 Serge Lang for his paper "Unramified class field theory over function fields in several variables" Maxwell...

field whose discriminant has at least 6 prime factors. Then the maximal unramified 2-extension of K has infinite degree. More generally, a number field with...

problem for bounded analytic functions, American Journal of Mathematics, volume 80 (1958), pp. 921–930; Interpolation by bounded analytic functions and the...