Uniformity in Mordell–Lang for curves
V Dimitrov, Z Gao, P Habegger - Annals of Mathematics, 2021 - projecteuclid.org
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 …
number field of degree d≥1. It has at most finitely many rational points by the Mordell …
Adelic line bundles on quasi-projective varieties
X Yuan, SW Zhang - arXiv preprint arXiv:2105.13587, 2021 - arxiv.org
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 …
finitely generated fields. Besides definitions of adelic line bundles, we consider their …
Equidistribution in families of abelian varieties and uniformity
L Kühne - arXiv preprint arXiv:2101.10272, 2021 - arxiv.org
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 …
Dimitrov, Gao, and Habegger, we deduce uniform results on the Manin-Mumford and the …
The Betti map associated to a section of an abelian scheme
Y André, P Corvaja, U Zannier - Inventiones mathematicae, 2020 - Springer
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 …
linear combination of the periods of A with real coefficients, the Betti coordinates of ξ ξ. When …
Dynamics on ℙ1: preperiodic points and pairwise stability
L DeMarco, NM Mavraki - Compositio Mathematica, 2024 - cambridge.org
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 …
the degree d, so that any pair of holomorphic maps II: Écart uniforme entre Lattès et …
[图书][B] Point-Counting and the Zilber–Pink Conjecture
J Pila - 2022 - books.google.com
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 …
to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink …
Arithmetic bigness and a uniform Bogomolov-type result
X Yuan - arXiv preprint arXiv:2108.05625, 2021 - arxiv.org
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 …
is a big adelic line bundle, and apply it to prove a uniform Bogomolov-type theorem for …
Heights and periods of algebraic cycles in families
We consider the Beilinson-Bloch heights and Abel-Jacobian periods of homologically trivial
Chow cycles in families. For the Beilinson-Bloch heights, we show that for any $ g\ge 3$, we …
Chow cycles in families. For the Beilinson-Bloch heights, we show that for any $ g\ge 3$, we …
The Ax–Schanuel conjecture for variations of mixed Hodge structures
Z Gao, B Klingler - Mathematische Annalen, 2024 - Springer
The Ax–Schanuel conjecture for variations of mixed Hodge structures | Mathematische
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Annalen Skip to main content SpringerLink Account Menu Find a journal Publish with us Track …