相关论文: A Database of Local Fields

We report on a database of field extensions of the rationals, its properties and the methods used to compute it. At the moment the database encompasses roughly 100,000 polynomials generating distinct number fields over the rationals, of…

In the present article, we introduce beta-expansions in the ring $\mathbb{Z}_p$ of $p$-adic integers. We characterise the sets of numbers with eventually periodic and finite expansions.

The first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic.

Let $p$ be a prime and let $\mathbb{Q}_p$ be the field of $p$-adic numbers. It is known that the finite extensions of $\mathbb{Q}_p$ of a given degree are finite up to isomorphism. Given a cubic field extension $L$ of $\mathbb{Q}_p$…

Current extragalactic databases are reviewed, including object-oriented databases, astronomical catalogues and compilations, as well as image archives and object catalogues from large-scale surveys. One challenge of the future will be to…

Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.

A complete list of one dimensional groups definable in the p-adic numbers is given, up to a finite index subroup and a quotient by a finite subgroup.

In this paper we find the genus field of finite abelian extensions of the global rational function field. We introduce the term conductor of constants for these extensions and determine it in terms of other invariants. We study the…

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.

This work presents author's explicit methods of constructing abelian extensions of complete discrete valuation fields. His approach to explicit equations of a cyclic extension of degree p^n which contains a given cyclic extension of degree…

The objective of this article is to give an introduction to p-adic analysis along the lines of Tate's thesis, as well as incorporating material of a more recent vintage, for example Weil groups.

We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.

We develop a notion of cell decomposition suitable for studying weak p- adic structures (reducts of p-adic fields where addition and multiplication are not (everywhere) definable). As an example, we apply this to a language with restricted…

The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…

In this paper, we define locally matchable subsets of a group which is extracted from the concept of matchings in groups and used as a tool to give alternative proofs for existing results in matching theory. We also give the linear analogue…

In this short survey we look at a few basic features of p-adic numbers, somewhat with the point of view of a classical analyst. In particular, with p-adic numbers one has arithmetic operations and a norm, just as for real or complex…

This document contains the notes of a lecture I gave at the "Journ\'ees Nationales du Calcul Formel" (JNCF) on January 2017. The aim of the lecture was to discuss low-level algorithmics for p-adic numbers. It is divided into two main parts:…

A database of abstract groups has been added to the L-functions and Modular Forms Database (LMFDB), available at https://www.lmfdb.org/Groups/Abstract/. We discuss the functionality of the database and what makes it distinct from other…

We extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion of local analysis meant to capture the behavior of these…

We introduce a spreading out technique to deduce finiteness results for \'etale fundamental groups of complex varieties by characteristic $p$ methods, and apply this to recover a finiteness result proven recently for local fundamental…