Langlands lambda function for quadratic tamely ramified extensions

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.

Decomposition types in minimally tamely ramified extensions of

PRESENTING GALOIS GROUPS OF INFINITE TAMELY RAMIFIED p-EXTENSIONS

Let p be a rational prime and S a finite set of rational primes. We are interested in the structure of GS(p), the Galois group of the maximal p-extension of Q unramified outside S (and ∞ if p = 2). In the case that p ∈ S, many GS(p) are known explicitly [12], but in the case that p ∈ S, very little is known. Throughout this report we shall assume that p ∈ S. The author developed methods to comp...

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...

Normic continued fractions in totally and tamely ramified extensions of local fields

The goal of this paper is to introduce a new way of constructing continued fractions in a Galois, totally and tamely ramified extension of local fields. We take a set of elements of a special form using the norm of that extension and we show that the set such defined is dense in the field by the means of continued fractions.