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

In this work we present some arithmetic properties of families of abelian $p$--extensions of global function fields, among which are their generators and their type of ramification and decomposition.

In this paper, extending our earlier program, we derive maximal canonical extensions for multiplicative summations into algebraically closed fields. We show that there is a well-defined analogue to minimal polynomials for a series algebraic…

In connection with our previous work on semi-galois categories, this paper proves an arithmetic analogue of Christol's theorem concerning an automata-theoretic characterization of when a formal power series over finite field is algebraic…

We provide several properties of the geometric polynomials discussed in earlier works of the authors. Further, the geometric polynomials are used to obtain a closed form evaluation of certain series involving Riemann's zeta function.

Let G be a semisimple group over an algebraically closed field of characteristic p>0. We give a (partly conjectural) simple, closed formula for the character of many indecomposable tilting rational G-modules, assuming that p is large.

Summation of a large class of the functional series, which terms contain factorials, is considered. We first investigated finite partial sums for integer arguments. These sums have the same values in real and all p-adic cases. The…

The classical Witt vectors are a ubiquitous object in algebra and number theory. They arise as a functorial construction that takes perfect fields k of prime characteristic p > 0 to p-adically complete discrete valuation rings of…

We study the Artin Approximation property with constraints in a different frame. As a consequence we give a nested Artin Strong Approximation property for algebraic power series rings over a field.

We compute the PI-exponent of the matrix ring with coefficients in an associative algebra. As a consequence, we prove the following. Let $\mathcal{R}$ be a PI-algebra with a positive PI-exponent. If $M_n(\mathcal{R})$ and $M_m(\mathcal{R})$…

The concept of a fully interlacing matrix of formal power series with real coefficients is introduced. This concept extends and strengthens that of an interlacing sequence of real-rooted polynomials with nonnegative coefficients, in the…

We show that for k a perfect field of characteristic p, there exist endomorphisms of the completed algebraic closure of k((t)) which are not bijective. As a corollary, we resolve a question of Fargues and Fontaine by showing that for p a…

In this paper, we define a q-adic factorial and we demonstrate some properties of a generalized p-adic gamma function. Also, some numerical examples have been given

Let $\mathbb{F}_{p^k}$ be a finite field of odd characteristic $p$. In this paper we give a classification, up to isomorphism, of the associative commutative $\mathbb{F}_{p^k}$-algebras, starting from the connection with their bi-brace…

In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. We extend its application to the case of formal power series over a field of arbitrary characteristic and illustrate the proposed approach…

Let $K$ be a finite extension of the field $\mathbb{Q}_p$ of $p$-adic numbers and $\O$ be its integral ring. The convergent power series with coefficients in $\O$ are studied as dynamical systems on $\O$. A minimal decomposition theorem for…

Hesselholt and Madsen in [7] define and study the (absolute, p-typical) de Rham-Witt complex in mixed characteristic, where p is an odd prime. They give as an example an elementary algebraic description of the de Rham-Witt complex over…

The p-cohomology of an algebraic variety in characteristic p lies naturally in the category $D_{c}^{b}(R)$ of coherent complexes of graded modules over the Raynaud ring (Ekedahl-Illusie-Raynaud). We study homological algebra in this…

Ordinary algebra of formal power series in one variable is convenient to study by means of the algebra of Riordan matrices and the Riordan group. In this paper we consider algebra of formal power series without constant term, isomorphic to…

We survey our recent work on an extension of the theory of motivic integration, called arithmetic motivic integration. We developed this theory to understand how p-adic integrals of a very general type depend on p.

We give a simple proof of the splitting lemma in singularity theory, also known as generalized Morse lemma, for formal power series over arbitrary fields. Our proof for the uniqueness of the residual part in any characteristic is new and…