Related papers: A characterization of strictly APF extensions

Let $X$ be an algebraic variety over a field $K \subset \overline{{\mathbb{Q}}_p}$ and $f$ be a self map. When $K$ is a local field, the boundedness of $f$-periods in $X(K)$ is a well studied question. We will study the same question for…

Let M be a field of finite type over {\bf Q} and X a variety defined over M. We study when the set {P \in X(K) \mid f^{\circ n} (P) = P for some n \geq 1} is finite for any finite extension fields K of M and for any dominant K-morphisms f :…

The p-class tower $F_p^\infty(k)$ of a number field k is its maximal unramified pro-p extension. It is considered to be known when the p-tower group, that is the Galois group $G:=Gal(F_p^\infty(k)/k)$, can be identified by an explicit…

In this paper we derive necessary and sufficient homological and cohomological conditions for profinite groups and modules to be of type $\operatorname{FP}_n$ over a profinite ring $R$, analogous to the Bieri-Eckmann criteria for abstract…

We prove that for any prime $p>2$, $q=p^\nu$ a power of $p$, $n\ge p$ and $G=S_n$ or $G=A_n$ (symmetric or alternating group) there exists a Galois extension $K/\mathbb F_q(T)$ ramified only over $\infty$ with $\mathrm{Gal}(K/\mathbb…

Let $S$ be a closed Riemann surface of genus $g \geq 2$ and $\varphi$ be a conformal automorphism of $S$ of prime order $p$ such that $S/\langle \varphi \rangle$ has genus zero. Let ${\mathbb K} \leq {\mathbb C}$ be a field of definition 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…

Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper. The results are given in terms of $L^p$ integrability of the function and its…

The objects of study in this paper are Hopf algebras $H$ which are finitely generated algebras over an algebraically closed field and are extensions of a commutative Hopf algebra by a finite dimensional Hopf algebra. Basic structural and…

Some aspects of a mathematical theory of rigidity and flexibility are developed for general infinite frameworks and two main results are obtained. In the first sufficient conditions, of a uniform local nature, are obtained for the existence…

Let K be a local field whose residue field is a finite field of characteristic p, and let L/K be a finite totally ramified Galois extension. Fried and Heiermann defined the "indices of inseparability" of L/K, a refinement of the…

In this paper we give a short, elementary proof of the following too extreme cases of the Leopoldt conjecture: the case when $\K/\Q$ is a solvable extension and the case when it is a totally real extension in which $p$ splits completely.…

Let K be a field of characteristic p>0, and let q be a power of p. We determine all polynomials f in K[t]\K[t^p] of degree q(q-1)/2 such that the Galois group of f(t)-u over K(u) has a transitive normal subgroup isomorphic to PSL_2(q),…

We construct a Galois correspondence for finite purely inseparable field extensions $F/K$, generalising a classical result of Jacobson for extensions of exponent one (where $x^p \in K$ for all $x\in F$).

Given a field $K$, a rational function $\phi \in K(x)$, and a point $b \in \mathbb{P}^1(K)$, we study the extension $K(\phi^{-\infty}(b))$ generated by the union over $n$ of all solutions to $\phi^n(x) = b$, where $\phi^n$ is the $n$th…

Building on work of J. Robinson and A. Shlapentokh, we develop a general framework to obtain definability and decidability results of large classes of infinite algebraic extensions of $\mathbb{F}_p(t)$. As an application, we show that for…

This paper gives examples of function fields $K_0$ over a finite field $\mathbb{F}_q$ of $p$ power order ramified only at one finite regular prime over $\mathbb{F}_q(t)$, which admit infinite Hilbert $p$-class field towers. Such a $K_0$ can…

For every prime $p\geq 5$ for which a certain condition on the class group $\text{Cl}(\mathbb{Q}(\mu_p))$ is satisfied, we construct a $p$-adic analytic Galois extension of the infinite cyclotomic extension $\mathbb{Q}(\mu_{p^{\infty}})$…

The main goal of this paper is to study some properties of an extension of valuations from classical invariants. More specifically, we consider a valued field $(K,\nu)$ and an extension $\omega$ of $\nu$ to a finite extension $L$ of $K$.…

Let $E$ be a field of absolute Brauer dimension abrd$(E)$, and $F/E$ a transcendental finitely-generated extension. This paper shows that the Brauer dimension Brd$(F)$ is infinite, if abrd$(E) = \infty $. When the absolute Brauer…