相关论文: Power series and p-adic algebraic closures

In this paper we study the Kummer extensions of the power series field $K=k((X_1,...,X_n)$, where $k$ is an algebraically closed field of arbitrary characteristic.

Given an algebraic ordinary differential equation (AODE), we propose a computational method to determine when a truncated power series can be extended to a formal power series solution. If a certain regularity condition on the given AODE or…

We study sets of integers that can be defined by the vanishing of a generalised polynomial expression. We show that this includes sets of values of linear recurrent sequences of Salem type and some linear recurrent sequences of Pisot type.…

We investigate some Galois groups of linearized polynomials over fields such as $\mathbb{F}_q(t)$. The space of roots of such a polynomial is a module for its Galois group. We present a realization of the symmetric powers of this module, as…

We prove that the main examples in the theory of algebraic differential equations possess a remarkable total differential overconvergence property. This allows one to consider solutions to these equations with coordinates in algebraically…

In the paper we prove for every finite algebra A that either it has the polynomially generated powers (PGP) property, or it has the exponentially generated powers (EGP) property. For idempotent algebras we give a simple criteria for the…

Using a generalized binomial transform and a novel binomial coefficient identity, we will show that the set of p-recursive sequences is closed under the binomial transform. Using these results, we will derive a new series representation for…

The twisted $T$-adic exponential sum associated to a polynomial in one variable is studied. An explicit arithmetic polygon is proved to be the generic Newton polygon of the twisted $C$-function of the T-adic exponential sum. It gives the…

Let $k$ be a perfect field of characteristic $p$ and set $K=k((t))$. In this paper we study the ramification properties of elements of Aut$_k(K)$. By choosing a uniformizer for $K$ we may interpret our theorems in terms of power series over…

Let R be an associative ring with possible extra structure. R is said to be weakly small if there are countably many 1-types over any finite subset of R. It is locally P if the algebraic closure of any finite subset of R has property P. It…

The functional decomposition of polynomials has been a topic of great interest and importance in pure and computer algebra and their applications. The structure of compositions of (suitably normalized) polynomials f=g(h) over finite fields…

Let $G$ be a connected reductive algebraic group with simply connected derived subgroup. Over the complex numbers there exists a local method to study the geometric properties of a point $g$ in the closure of a Jordan class of $G$ in terms…

Let $A$ be a central quantization of an affine Poisson variety $X$ over a field of characteristic $p>0.$ We show that the completion of $A$ with respect to a closed point $y\in X$ is isomorphic to the tensor product of the Weyl algebra with…

In this paper some classes of local polynomial functions on abelian groups are characterized by the properties of their variety. For this characterization we introduce a numerical quantity depending on the variety of the local polynomial…

We classify all linearly compact simple Jordan superalgebras over an algebraically closed field of characteristic zero. As a corollary, we deduce the classification of all linearly compact unital simple generalized Poisson superalgebras.

Motivated by the study of algebraic classes in mixed characteristic we define a countable subalgebra of $\bar{\mathbb{Q}}_p$ which we call the algebra of Andr\'e's $p$-adic periods. We construct a tannakian framework to study these periods.…

In this paper, we consider a general form of the analogue of Ramanujan's sum in the ring of polynomials over a finite field. We first prove some multiplicative properties of such functions before considering their finite Fourier series and…

Let $\cal R$ be either the Grothendieck semiring (semiring with multiplication) of complex algebraic varieties, or the Grothendieck ring of these varieties, or the Grothendieck ring localized by the class of the complex affine line. We…

The purpose of this paper is to study finite-dimensional Lie algebras over a field k of characteristic zero which admit a commutative polarization (CP). Among the many results and examples, it is shown that, if k is algebraically closed,…

We establish a condition (so called generalized entropic property), equivalent to the fact that for every algebra A from a given variety V, the set of all subalgebras of A is a subuniverse of the complex algebra of A. We investigate the…