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 …

In this paper, we establish a theory of adelic line bundles over quasi-projective varieties over
finitely generated fields. Besides definitions of adelic line bundles, we consider their …

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 …

Let satisfies some conditions); it is an important step to prove the bound for the number of
rational points on curves (Dimitrov et al., Uniformity in Mordell–Lang for Curves, Preprint …

An endomorphism f: P k→ Pk of degree d≥ 2 is said to be postcritically finite (or PCF) if its
critical set Crit (f) is preperiodic, ie if there are integers m> n≥ 0 such that fm (Crit (f))⊆ fn …

We establish the Geometric Dynamical Northcott Property for polarized endomorphisms of a
projective normal variety over a function field $\mathbf {K} $ of characteristic zero. This …

We initiate the study of random iteration of automorphisms of real and complex projective
surfaces, as well as compact Kähler surfaces, focusing on the classification of stationary …

On an abelian scheme over a smooth curve over Q a symmetric relatively ample line bundle
defines a fiberwise Néron--Tate height. If the base curve is inside a projective space, we …

We introduce a new approach to the geometric Bombieri--Lang conjecture for hyperbolic
varieties in characteristic 0. The main idea is to construct an entire curve on a special fiber of …

Geometric Bogomolov conjecture in arbitrary characteristics | Inventiones mathematicae
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