This book considers the so-called Unlikely Intersections, a topic that embraces well-known
issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of …

We present a new proof of the Manin–Mumford conjecture about torsion points on algebraic
subvarieties of abelian varieties. Our principle, which admits other applications, is to view …

In this article I state and prove some basic results about Salem numbers, and then survey
some of the literature about them. My intention is to complement other general treatises on …

Mahler measure, a height function for polynomials, is the central theme of this book. It has
many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is …

These lecture notes originate from a course delivered at the Scuola Normale in Pisa in 2006.
Generally speaking, the prerequisites do not go beyond basic mathematical material and …

We announce the classification of Sato-Tate groups of abelian threefolds over number fields;
there are 410 possible conjugacy classes of closed subgroups of USp (6) that occur. We …

This document is intended to summarize the theory and methods behind fq_isog collection
inside the ab_var database in the LMFDB as well as some observations gleaned from these …

arxiv:1607.01530v1 [math.NT] 6 Jul 2016 Page 1 arxiv:1607.01530v1 [math.NT] 6 Jul 2016
MARKOFF SURFACES AND STRONG APPROXIMATION: 1 JEAN BOURGAIN, ALEXANDER …

Until recently, no Salem numbers were known of trace below-1. In this paper we provide
several examples of trace-2, including an explicit infinite family. We establish that the …

We consider a rational function f which is 'lacunary'in the sense that it can be expressed as
the ratio of two polynomials (not necessarily coprime) having each at most a given number l …