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

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 −...

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...

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...

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...

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

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

project led by Dennis Gaitsgory announced a proof of the (categorical, unramified) geometric Langlands conjecture leveraging Hecke eigensheaf as part of...

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...

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

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...

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...

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...

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...

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...

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...

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...

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

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...

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...

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...

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...

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...

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

{\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...