Consider a smooth, geometrically irreducible, projective curve of genus g≥2 defined over a
number field of degree d≥1. It has at most finitely many rational points by the Mordell …

Using equidistribution techniques from Arakelov theory as well as recent results obtained by
Dimitrov, Gao, and Habegger, we deduce uniform results on the Manin-Mumford and the …

arXiv:2105.15085v2 [math.NT] 24 Jul 2021 Page 1 arXiv:2105.15085v2 [math.NT] 24 Jul 2021
THE UNIFORM MORDELL–LANG CONJECTURE ZIYANG GAO, TANGLI GE AND LARS …

DeMarco, Krieger, and Ye conjectured that there is a uniform bound B, depending only on
the degree d, so that any pair of holomorphic maps II: Écart uniforme entre Lattès et …

We prove that Zhang's dynamical Bogomolov conjecture holds uniformly along $1 $-
parameter families of rational split maps and curves. This provides dynamical analogues of …

We deduce an analogue of the Bogomolov conjecture for non-degenerate subvarieties in
fibered products of families of elliptic curves from the author's recent theorem on …

We propose a formulation of the relative Bogomolov conjecture and show that it gives an
affirmative answer to a question of Mazur's concerning the uniformity of the Mordell–Lang …

Let K be a finitely generated field. We construct an n-dimensional linear system L of
hypersurfaces of degree d in P n defined over K such that each member of L defined over K …

We study the dynamics of algebraic families of maps on $\mathbb {P}^ N $, over the field
$\mathbb {C} $ of complex numbers, and the geometry of their preperiodic points. The goal …

We study the dynamics of algebraic families of maps on Pn, over the field C of complex
numbers, and the geometry of their preperiodic points. The goal of this note is to formulate a …