Related papers: Abelian $p$-extensions and additive polynomials

Let $p$ be a prime number and let $K$ be a finite extension of the field $\mathbb{Q}_p$ of $p$-adic numbers. Let $N$ be a fully ramified, elementary abelian extension of $K$. Under a mild hypothesis on the extension $N/K$, we show that…

Given a $p$-adic field $K$ and a prime number $\ell$, we count the total number of the isomorphism classes of $p^\ell$-extensions of $K$ having no intermediate fields. Moreover for each group that can appear as Galois group of the normal…

Let $F$ be a global function field of characteristic $p>0$, $K/F$ an $\ell$-adic Lie extension ($\ell\neq p$) and $A/F$ an abelian variety. We provide Euler characteristic formulas for the $Gal(K/F)$-module $Sel_A(K)_\ell$.

This article aims to reinforce the broad applicability of the umbral approach to address complex mathematical challenges and contribute to various scientific and engineering endeavors. The umbral methods are used to reformulate the…

This paper contains three parts. In the first part, we give a thorough overview of the theory of Artin-Schreier-Witt extensions: this theory allows one to understand the $\mathbf{Z}/p^n\mathbf{Z}$-extensions of any field $K$ of…

We investigate criteria for algebra extensions that are of Galois type with respect to the coaction of a Hopf algebra or, more generally, a one-sided quotient of a Hopf algebra, or with respect to an entwining. We study the module- and…

We obtain a lifting property for finite quotients of algebraic groups, and applications to the structure of these groups.

We survey some important properties of fields of generalized series and of exponential-logarithmic series, with particular emphasis on their possible differential structure, based on a joint work of the author with S. Kuhlmann [KM12b,KM11].

Some important properties of the chromatic polynomial also hold for any polynomial set map satisfying p_S(x+y)=\sum_{T\uplus U=S}p_T(x)p_U(y). Using umbral calculus, we give a formula for the expansion of such a set map in terms of any…

Our goal in this work is to found a closed form for rational generat- ing functions, these generate a various families of polynomials and generalized polynomials, in order to get the general recursive formula satisfied by these polynomials.

Let $G$ be a connected complex algebraic group and $A$ a connected abelian algebraic group endowed with an algebraic action of $G$ by group automorphisms. In the present note we describe the abelian group $\Ext_{alg}(G,A)$ of algebraic…

In this paper we obtain the genus field of a general Kummer extension of a global rational function field. We study first the case of a general Kummer extension of degree a power of a prime. Then we prove that the genus field of a composite…

Let $p$ and $q$ be odd prime numbers. In this paper we study non-abelian pq-fold regular covers of the projective line, determine algebraic models for some special cases and provide a general isogeny decomposition of the corresponding…

In this article, we consider some generalizations of polynomial and exponential B-splines. Firstly, the extension from integral to complex orders is reviewed and presented. The second generalization involves the construction of uncountable…

We show that the coefficients of rational 2-functions are contained in an abelian number field. More precisely, we show that the poles of such functions are poles of order one and given by roots of unity and rational residue.

We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one free parameter to them. In particular, we generalize generating functions for the Askey-Wilson, continuous…

A major open problem in current Galois theory is to characterize those profinite groups which appear as absolute Galois groups of various fields. Obtaining detailed knowledge of the structure of quotients and subgroup filtrations of Galois…

We prove a classification of additive polynomial superfunctors, which allows us to compute some extensions of a superfunctor of the form $F \circ A$ where $F$ is a classical polynomial functor and $A$ is additive. We get a formula which…

We introduce a general constructive method to find a p-basis (and the Ulm invariants) of a finite Abelian p-group M. This algorithm is based on Groebner bases theory. We apply this method to determine the additive structure of…

We study the structure of an algebraically closed field with extra function resembling the classical exponentiation on complex numbers.