Related papers: On totally ramified extensions of discrete valued …

We construct explicitly APF extensions of finite extensions of $\qp$ for which the Galois group is not a p-adic Lie group and which do not have any open subgroup with $\zp$-quotient.

For a simple, normal and finite extension of a valued field, we prove that we can related the order of the ramification group of the field extension and the set of key polynomials associated to the extension of the valuation. More…

Author's generalization of one-dimensional class field theory to theory of abelian totally ramified p-extensions of a complete discrete valuation field with arbitrary non-separably p-closed residue field and its applications are described.

Let K be a local field of characteristic p with perfect residue field k. In this paper we find a set of representatives for the k-isomorphism classes of totally ramified separable extensions L/K of degree p. This extends work of Klopsch,…

We give a purely scheme theoretic construction of the filtration by ramification groups of the Galois group of a covering. The valuation need not be discrete but the normalizations are required to be locally of complete intersection.

A generalization of Serre's Conjecture asserts that if $F$ is a totally real field, then certain characteristic $p$ representations of Galois groups over $F$ arise from Hilbert modular forms. Moreover it predicts the set of weights of such…

Let $K$ be a complete discretely valued field. An extension $L/K$ is "weakly totally ramified" if the residue extension is purely inseparable. We sharpen a result of Ax by showing that any Galois-invariant disk in the algebraic closure of…

We determine all the $p$-adic analytic groups that are realizable as Galois groups of the maximal pro-$p$ extensions of number fields with prescribed ramification and splitting under an assumption which allows us to move away from the Tame…

Let $K$ be a number field defined by a monic irreducible polynomial $F(X) \in \mathbb{Z}[X]$, $p$ a fixed rational prime, and $\nu_p$ the discrete valuation associated to $p$. Assume that $\overline{F}(X)$ factors modulo $p$ into the…

Let K be a complete discrete valuation field of mixed characteristic (0,p) with algebraically closed residue field, and let f: Y --> P^1 be a three-point G-cover defined over K, where G has a cyclic p-Sylow subgroup P. We examine the stable…

Let K be a local field of mixed characteristic not absolutely ramified. Fontaine-Laffaille theory gives a description of the torsion crystalline Z_p-representations of the absolute Galois group of K (p denotes the characteristic of the…

The wild group is the group of wild automorphisms of a local field of characteristic p. In this paper we apply Fontaine-Wintenberger's theory of fields of norms to study the structure of the wild group. In particular we provide a new short…

For a given positive integer $n$ and $K/\mathbb{Q}_p$ a finite extension of ramification degree $e$, we determine the number of finite Galois extensions $L/K$ with inertia degree $f$ and a single nonnegative ramification jump at $n$ as long…

We construct various explicit Herr complexes that compute the Galois cohomology of a $p$-adic representation of the absolute Galois group of a complete discrete valuation field of characteristic $0$ with a perfect residue field of…

Ramification theory of monogenic extensions of complete discrete valuation fields is presented. Relations to Kato's conductor are discussed.

Given a hilbertian field $k$ of characteristic zero and a finite Galois extension $E/k(T)$ with group $G$ such that $E/k$ is regular, we produce some specializations of $E/k(T)$ at points $t_0 \in \mathbb{P}^1(k)$ which have the same Galois…

Let k be a complete discrete valuation field of equal characteristic p>0. Using the tools of p-adic differential modules, we define refined Artin and Swan conductors for a representation of the absolute Galois group $G_k$ with finite local…

For a smooth surface X over an algebraically closed field of positive characteristic, we consider the ramification of an Artin-Schreier extension of X. A ramification at a point of codimension 1 of X is understood by the Swan conductor. A…

We present a characterization of differential Picard-Vessiot extensions which is analogous to the field theoretic characterization of Galois extensions in classical Galois theory.

Let L/K be a finite Galois extension of complete local fields with finite residue fields and let G=Gal(L/K). Let G_1 and G_2 be the first and second ramification groups. Thus L/K is tamely ramified when G_1 is trivial and we say that L/K is…