Finitely ramified iterated extensions

Let K be a number field, t a parameter, F=K(t) and f in K[x] a polynomial of degree d. The polynomial P_n(x,t)= f^n(x) - t in F[x] where f^n is the n-fold iterate of f, is absolutely irreducible over F; we compute a recursion for its discriminant. Let L=L(f) be the field obtained by adjoining to F all roots, in a fixed algebraic closure, of P_n for all n; its Galois group Gal(L/F) is the iterated monodromy group of f. The iterated extension L/F is finitely ramified if and only if f is post-critically finite (pcf). We show that, moreover, for pcf polynomials f, every specialization of L/F at t=t_0 in K is finitely ramified over K, pointing to the possibility of studying Galois groups with restricted ramification via tree representations associated to iterated monodromy groups of pcf polynomials. We discuss the wildness of ramification in some of these representations, describe prime decomposition in terms of certain finite graphs, and also give some examples of monogene number fields.Comment: 19 page

Tamely Ramified Towers and Discriminant Bounds for Number Fields—II

AbstractThe root discriminant of a number field of degree n is the n th root of the absolute value of its discriminant. Let R0(2 m) be the minimal root discriminant for totally complex number fields of degree 2 m, and put α0=lim infmR0(2 m). DefineR1 (m) to be the minimal root discriminant of totally real number fields of degree m and put α1=lim infmR1(m). Assuming the Generalized Riemann Hypothesis, α0≥ 8 πe\gamma≈ 44.7, and,α1 ≥ 8πe\gamma+π/2 ≈ 215.3. By constructing number fields of degree 12 with suitable properties, we give the best known upper estimates for α0andα1 : α0< 82.2,α1 < 954.3

Sur la séparation des caractères par les Frobenius

In this paper, we are interested in the question of separating two characters of the absolute Galois group of a number field K, by the Frobenius of a prime ideal p of OK. We first recall an upper bound for the norm N(p) of the smallest such prime p, depending on the conductors and on the degrees. Then we give two applications: (i) find a prime number p for which P (mod p) has a certain type of factorization in Fp[X], where P ∈ Z[X] is a monic, irreducible polynomial of squarefree discriminant; (ii) on the estimation of the maximal number of tamely ramified extensions of Galois group An over a fixed number field K. To finish, we discuss some statistics in the quadratic number fields case (real and imaginary) concerning the separation of two irreducible unramified characters of the alterning group An,for n = 5, 7, 13.In this paper, we are interested in the question of separating two characters of the absolute Galois group of a number field K, by the Frobenius of a prime ideal p of OK. We first recall an upper bound for the norm N(p) of the smallest such prime p, depending on the conductors and on the degrees. Then we give two applications: (i) find a prime number p for which P (mod p) has a certain type of factorization in Fp[X], where P ∈ Z[X] is a monic, irreducible polynomial of squarefree discriminant; (ii) on the estimation of the maximal number of tamely ramified extensions of Galois group An over a fixed number field K. To finish, we discuss some statistics in the quadratic number fields case (real and imaginary) concerning the separation of two irreducible unramified characters of the alterning group An,for n = 5, 7, 13.In this paper, we are interested in the question of separating two characters of the absolute Galois group of a number field K, by the Frobenius of a prime ideal p of OK. We first recall an upper bound for the norm N(p) of the smallest such prime p, depending on the conductors and on the degrees. Then we give two applications: (i) find a prime number p for which P (mod p) has a certain type of factorization in Fp[X], where P ∈ Z[X] is a monic, irreducible polynomial of squarefree discriminant; (ii) on the estimation of the maximal number of tamely ramified extensions of Galois group An over a fixed number field K. To finish, we discuss some statistics in the quadratic number fields case (real and imaginary) concerning the separation of two irreducible unramified characters of the alterning group An,for n = 5, 7, 13

Wage Dispersion and Decentralization of Wage Bargaining

This paper studies how decentralization of wage bargaining from sector to firm-level influences wage levels and wage dispersion. We use detailed panel data covering a period of decentralization in the Danish labor market. The decentralization process provides variation in the individual worker's wage-setting system that facilitates identification of the effects of decentralization. We find a wage premium associated with firm-level bargaining relative to sector-level bargaining, and that the return to skills is higher under the more decentralized wage-setting systems. Using quantile regression, we also find that wages are more dispersed under firm-level bargaining compared to more centralized wage-setting systems.wage bargaining, decentralization, wage dispersion

Wage Dispersion and Decentralization of Wage Bargaining

This paper studies how decentralization of wage bargaining from sector to firm level influences wage levels and wage dispersion. We use a detailed panel data set covering a period of decentralization in the Danish labor market. The decentralization process provides exogenous variation in the individual worker's wage-setting system that facilitates identification of the effects of decentralization. Consistent with predictions we find that wages are more dispersed under firm-level bargaining compared to more centralized wage-setting systems. However, the differences across wage-setting systems are reduced substantially when controlling for unobserved individual level heterogeneity.Wage bargaining; decentralization; panel data quantile regression