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 …

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 …

The Ax–Schanuel conjecture for variations of mixed Hodge structures | Mathematische
Annalen Skip to main content SpringerLink Account Menu Find a journal Publish with us Track …

In this paper we prove the mixed Ax–Schanuel theorem for the universal abelian varieties
(more generally any mixed Shimura variety of Kuga type), and give some simple …

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 …

A translation surface is a multifaceted object that can be studied with the tools of dynamics,
analysis, or algebraic geometry. Moduli spaces of translation surfaces exhibit equally rich …

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 …