Related papers: Short models of global fields
Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such…
We give an elementary construction of an arbitrary differentially closed field and of a universal differential extension of a differential field in terms of Nash function fields. We also give a characterization of any Archimedean ordered…
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
We study some problems in metric Diophantine approximation over local fields of positive characteristic.
We present a survey of some aspects and new results on configurations, i.e. disjoint unions of constellations of infinitely near points, local and global theory, with some applications and results on generalized Enriques diagrams, singular…
We present a new method for the reconstruction of rational functions through finite-fields sampling that can significantly reduce the number of samples required. The method works by exploiting all the independent linear relations among…
We define standardized constructions of finite fields, and standardized generators of (multiplicative) cyclic subgroups in these fields. The motivation is to provide a substitute for Conway polynomials which can be used by various software…
We investigate the mathematical structure of the world sheet in two-dimensional conformal field theories.
In this paper are briefly outlined the motivations, mathematical ideas in use, pre-formalization and assumptions, object-as-functor construction, `soft' types and concept constructions, case study for concepts based on variable domains,…
We construct 3-dimensional once-Extended Topological Quantum Field Theories (ETQFTs for short) out of (possibly non-semisimple) modular categories, and we explicitly identify linear categories and functors in their image. The circle…
We present necessary and sufficient conditions to have global hypoellipticity and global solvability for a class of vector fields defined on a product of compact Lie groups. In view of Greenfield's and Wallach's conjecture, about the…
The purpose of this note is twofold. First, we survey results on the construction of large class groups of number fields by specialization of finite covers of curves. Then we give examples of applications of these techniques.
In this short note we provide a few examples of non-isomorphic arithmetically equivalent global function fields. These examples are obtained via well-known technique of adjoining the torsion points of various Drinfeld Modules to realise the…
We introduce a class of random fields that can be understood as discrete versions of multi-colour polygonal fields built on regular linear tessellations. We focus fir st on consistent polygonal fields, for which we show Markovianity and…
Several results related to flat Friedmann-Lema\^{\i}tre-Robertson-Walker models in the conformal (Einstein) frame of scalar-tensor gravity theories are extended. Scalar fields with arbitrary (positive) potentials and arbitrary coupling…
We prove that rationally connected varieties over the function field of a complex curve satisfy weak approximation for places of good reduction.
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
We introduce the notion of functionally compact sets into the theory of nonlinear generalized functions in the sense of Colombeau. The motivation behind our construction is to transfer, as far as possible, properties enjoyed by standard…
We develop a method to construct elusive functions using techniques of commutative algebra and algebraic geometry. The key notions of this method are elusive subsets and evaluation mappings. We also develop the effective elimination theory…
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.