Related papers: The valuation criterion for normal basis generator…

Let $(K,v)$ be a valued field. Take an extension of $v$ to a fixed algebraic closure $L$ of $K$. In this paper we show that an element $a\in L$ admits a complete distinguished chain over $K$ if and only if the extension $(K(a)|K,v)$ is…

In this paper we use the Galois module structure for the classical parameterizing spaces for elementary p-abelian extensions of a field K to give necessary and sufficient conditions for the solvability of any embedding problem which is an…

We consider a random field, defined on an integer-valued d-dimensional lattice, with covariance function satisfying a condition more general than summability. Such condition appeared in the well-known Newman's conjecture concerning the…

We demonstrate that the classical Michael selection theorem for l.s.c. mappings with a collectionwise normal domain can be reduced only to compact-valued mappings modulo Dowker's extension theorem for such spaces. The idea used to achieve…

Let $K$ be an algebraic number field with ring of integers $\Cal{O}_{K}$, $p>2$ be a rational prime and $G$ be the cyclic group of order $p $. Let $\Lambda$ denote the order $\Cal{O}_{K}[G].$ Let $Cl(\Lambda)$ denote the locally free class…

A classical theorem of P. McMullen describes all valuations on polytopes that are invariant under translations and weakly continuous, i.e., continuous with respect to parallel displacements of the facets of a polytope. While it is typically…

We prove a local-global principle for the embedding problems of global fields with restricted ramification. By this local-global principle, for a global field $k$, we use only the local information to give a presentation of the maximal…

Let $K/F$ be a finite Galois extension of number fields. It is well known that the Tchebotarev density theorem implies that an irreducible, finitely ramified $p$-adic representation $\rho$ of the absolute Galois group of $K$ is determined…

We contribute to the Malle conjecture on the number N (K, G, y) of finite Galois extensions E of some number field K of finite group G and of discriminant of norm |N K/Q (d E)| $\le$ y. We prove the lower bound part of the conjecture for…

We prove that if $K/\mathbb{Q}$ is a Galois extension of finite exponent and $K^{(d)}$ is the compositum of all extensions of $K$ of degree at most $d$, then $K^{(d)}$ has the Bogomolov property and the maximal abelian subextension of…

A number field $K$ is Hilbert-Speiser if all of its tame abelian extensions $L/K$ admit NIB (normal integral basis). It is known that $\mathbb{Q}$ is the only such field, but when we restrict $\text{Gal}(L/K)$ to be a given group $G$, the…

We prove that certain classical groups $G\subseteq {\rm GL}(d,\mathbb{R}^d)$ serve to characterize ordinary polynomials in $d$ real variables as elements of finite-dimensional subspaces of $C(\mathbb{R}^d)$ that are invariant by changes of…

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…

In this paper we study standard bases for submodules of K[[t_1,...,t_m]][x_1,...,x_n]^s respectively of their localisation with respect to a t-local monomial ordering. The main step is to prove the existence of a division with remainder…

We let R be an o-minimal expansion of a field, V a convex subring, and $(R_0, V_{0})$ an elementary substructure of (R,V). We let L be the language consisting of a language for R, in which R has elimination of quantifiers, and a predicate…

Explicit descriptions of local integral Galois module generators in certain extensions of $p$-adic fields due to Pickett have recently been used to make progress with open questions on integral Galois module structure in wildly ramified…

This paper introduces a natural extension of Kolchin's differential Galois theory to positive characteristic iterative differential fields, generalizing to the non-linear case the iterative Picard-Vessiot theory recently developed by Matzat…

Let K be a field and \ell be a prime such that char K \neq \ell. In the presence of sufficiently many roots of unity in K, we show how to recover some of the inertia/decomposition structure of valuations inside the maximal (\Z/\ell)-abelian…

Let $C \langle \boldsymbol{t} \rangle$ be the differential field generated by $l$ differential indeterminates $\boldsymbol{t}=(t_1, \dots, t_l)$ over an algebraically closed field $C$ of characteristic zero. In this article we present an…

Consider $d$ commuting $C_{0}$-semigroups (or equivalently: $d$-parameter $C_{0}$-semigroups) over a Hilbert space for $d \in \mathbb{N}$. In the literature (\textit{cf.} [29, 26, 27, 23, 18, 25]), conditions are provided to classify the…