Related papers: A Database of Local Fields
We develop a continued fraction algorithm in finite extensions of $\Q_p$ generalising certain algorithms in $\Q_p$, and prove the finiteness property for certain small degree extensions. We also discuss the metrical properties of the…
polyDB is a database for discrete geometric objects. The database is accessible via web and an interface from the software package polymake. It contains various datasets from the area of lattice polytopes, combinatorial polytopes, matroids…
Given primes $\ell\ne p$, we record here a $p$-adic valued Fourier theory on a local field over $\mathbf{Q}_\ell$, which is developed under the perspective of group schemes. As an application, by substituting rigid analysis for complex…
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
We investigate when a computable automorphism of a computable field can be effectively extended to a computable automorphism of its (computable) algebraic closure. We then apply our results and techniques to study effective embeddings of…
In this paper, we describe restricted one-dimensional central extensions of all finite dimensional simple restricted Lie algebras defined over fields of characteristic $p\ge 5$.
We study when the property that a field is dense in its real and p-adic closures is elementary in the language of rings and deduce that all models of the theory of algebraic fields have this property.
The goal is to obtain an asymptotic formula for the number of quadratic extensions with bounded discriminant of a some quadratic number field with odd class number. This extends an already known result for Q.
We investigate connections between local tameness of a group and a number of its ends.
A finite semifield is a division algebra over a finite field where multiplication is not necessarily associative. We consider here the complexity of the multiplication in small semifields and finite field extensions. For this operation, the…
In this paper, we give an overview of the various general methods in computing the zeta function of an algebraic variety defined over a finite field, with an emphasis on computing the reduction modulo $p^m$ of the zeta function of a…
Let $p$ be a prime. We discuss methods of solution of congruences modulo $p^n$ using $p$-adic numbers; these methods are similar to computations with real numbers (local methods). Examples of relations between local and global methods are…
We associate canonical virtual motives to definable sets over a field of characteristic zero. We use this construction to show that very general p-adic integrals are canonically interpolated by motivic ones.
A process of extending sets which can be used as foundation for an alternative organization for Differential and Integral Calculus is presented.
We give a characterization of ramification groups of local fields with imperfect residue fields, using those for local fields with perfect residue fields. As an application, we reprove an equality of ramification groups for abelian…
In this paper, the author proved that the base change lifting associated to a totally ramified extension of a non-archimedean local field coincides with a map coming from the close fields theory of Kazhdan under some conditions. As a…
We give an introduction to the "categorical" approach to the p-adic Langlands program, in both the "Banach" and "analytic" settings.
A complete p-adic Khintchine type theorem for approximation by p-adic algebraic numbers is established.
Many databases on the web are "hidden" behind (i.e., accessible only through) their restrictive, form-like, search interfaces. Recent studies have shown that it is possible to estimate aggregate query answers over such hidden web databases…
We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…