Tamely Ramified Morphisms of Curves and Belyi’s Theorem in Positive Characteristic

Tamely Ramified Extension’s Structure

The structure of an algebraic tamely ramified extension of a henselian valued field is studied. We will prove, in theorem 3.2, the following statement: A finite extension L/K is tamely ramified if and only if the field L is obtained from the maximal unramified extension T by adjoining the radicals m √ t, with t ∈ T, m ∈ N, m ≥ 1, (m, p) = 1, where p is the characteristic of the residue class fi...

Decomposition types in minimally tamely ramified extensions of

Galois groups of tamely ramified p - extensions par Nigel BOSTON

Very little is known regarding the Galois group of the maximal p-extension unramified outside a finite set of primes S of a number field in the case that the primes above p are not in S. We describe methods to compute this group when it is finite and conjectural properties of it when it is infinite.

Tamely Ramified Towers and Discriminant Bounds for Number Fields-II

The root discriminant of a number field of degree n is the nth root of the absolute value of its discriminant. Let R0(2m) be the minimal root discriminant for totally complex number fields of degree 2m, and put α0 = lim infmR0(2m). Define R1(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, α...

Tamely Ramified Towers and Discriminant Bounds for Number Fields

The root discriminant of a number field of degree n is the nth root of the absolute value of its discriminant. Let R2m be the minimal root discriminant for totally complex number fields of degree 2m, and put α0 = lim infmR2m. One knows that α0 ≥ 4πeγ ≈ 22.3, and, assuming the Generalized Riemann Hypothesis, α0 ≥ 8πeγ ≈ 44.7. It is of great interest to know if the latter bound is sharp. In 1978,...