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 …

Given a point ξ ξ on a complex abelian variety A, its abelian logarithm can be expressed as a
linear combination of the periods of A with real coefficients, the Betti coordinates of ξ ξ. When …

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 …

Point-counting results for sets in real Euclidean space have found remarkable applications
to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink …

In this paper, we prove that the admissible canonical bundle of the universal family of curves
is a big adelic line bundle, and apply it to prove a uniform Bogomolov-type theorem for …

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 …

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 …

Let k be an algebraically closed field. Let B be an irreducible normal projective variety over k
of dimension dB 1. Let K WD k. B/be the function field of B. Let A be an abelian variety …