ﻻ يوجد ملخص باللغة العربية
Let $varphi: {mathbb P}^1 longrightarrow {mathbb P}^1$ be a rational map of degree greater than one defined over a number field $k$. For each prime ${mathfrak p}$ of good reduction for $varphi$, we let $varphi_{mathfrak p}$ denote the reduction of $varphi$ modulo ${mathfrak p}$. A random map heuristic suggests that for large ${mathfrak p}$, the proportion of periodic points of $varphi_{mathfrak p}$ in ${mathbb P}^1({mathfrak o}_k/{mathfrak p})$ should be small. We show that this is indeed the case for many rational functions $varphi$.
We develop a theory of semidirect products of partial groups and localities. Our concepts generalize the notions of direct products of partial groups and localities, and of semidirect products of groups.
It is an open problem whether definability in Propositional Dynamic Logic (PDL) on forests is decidable. Based on an algebraic characterization by Bojanczyk, et. al.,(2012) in terms of forest algebras, Straubing (2013) described an approach to PDL ba
Let $k$ be a number field. In the spirit of a result by Yongqi Liang, we relate the arithmetic of rational points over finite extensions of $k$ to that of zero-cycles over $k$ for Kummer varieties over $k$. For example, for any Kummer variety $X$ ove
We consider the finitely generated groups acting on a regular tree with almost prescribed local action. We show that these groups embed as cocompact irreducible lattices in some locally compact wreath products. This provides examples of finitely gene
Let $m$ be a positive integer and let $Omega$ be a finite set. The $m$-closure of $Gle$Sym$(Omega)$ is the largest permutation group on $Omega$ having the same orbits as $G$ in its induced action on the Cartesian product $Omega^m$. The exact formula