منابع مشابه
Computing Ray Class Groups, Conductors and Discriminants
We use the algorithmic computation of exact sequences of Abelian groups to compute the complete structure of (ZK/m)∗ for an ideal m of a number field K, as well as ray class groups of number fields, and conductors and discriminants of the corresponding Abelian extensions. As an application we give several number fields with discriminants less than previously known ones. The paper is divided as ...
متن کاملRamification Groups and Artin Conductors of Radical Extensions of Q
We study the ramification properties of the extensions Q(ζm, m √ a)/Q under the hypothesis that m is odd and if p | m than either p ∤ vp(a) or pvp(m) | vp(a) (vp(a) and vp(m) are the exponents with which p divides a and m). In particular we determine the higher ramification groups of the completed extensions and the Artin conductors of the characters of their Galois group. As an application, we...
متن کامل779 – 816 Ramification groups and Artin conductors of radical extensions of Q par Filippo VIVIANI
We study the ramification properties of the extensions Q(ζm, m √ a)/Q under the hypothesis that m is odd and if p | m than either p vp(a) or pp | vp(a) (vp(a) and vp(m) are the exponents with which p divides a and m). In particular we determine the higher ramification groups of the completed extensions and the Artin conductors of the characters of their Galois group. As an application, we give ...
متن کاملDiscriminants and nonnegative polynomials
For a semialgebraic set K in R, let Pd(K) = {f ∈ R[x]≤d : f(u) ≥ 0 ∀u ∈ K} be the cone of polynomials in x ∈ R of degrees at most d that are nonnegative on K. This paper studies the geometry of its boundary ∂Pd(K). When K = R n and d is even, we show that its boundary ∂Pd(K) lies on the irreducible hypersurface defined by the discriminant ∆(f) of f . When K = {x ∈ R : g1(x) = · · · = gm(x) = 0}...
متن کاملDiscriminants and Ramified Primes
has some ei greater than 1. If every ei equals 1, we say p is unramified in K. Example 1.1. In Z[i], the only prime which ramifies is 2: (2) = (1 + i)2. Example 1.2. Let K = Q(α) where α is a root of f(X) = T 3 − 9T − 6. Then 6 = α3 − 9α = α(α− 3)(α+ 3). For m ∈ Z, α+m has minimal polynomial f(T −m) in Q[T ], so NK/Q(α+m) = −f(−m) = m3 − 9m+ 6 and the principal ideal (α−m) has norm N(α−m) = |m ...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2016
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle-2014-0022