The Erdős–Ulam problem, Lang's conjecture and uniformity

DOI10.1112/blms.12381zbMath1471.11202arXiv1901.02616OpenAlexW3106205541WikidataQ122975299 ScholiaQ122975299MaRDI QIDQ5855921

Kenneth Ascher, Lucas Braune, Amos Turchet

Publication date: 22 March 2021

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.02616

zbMATH Keywords

uniformityErdős-Ulam problem

Mathematics Subject Classification ID

Rational points (14G05) Singularities of surfaces or higher-dimensional varieties (14J17) Varieties over global fields (11G35) Surfaces of general type (14J29) Erd?s problems and related topics of discrete geometry (52C10)

Related Items (5)

Lang-Vojta conjecture over function fields for surfaces dominating \(\mathbb{G}_m^2\) ⋮ Integral distances from (two) given lattice points ⋮ On the number of perfect triangles with a fixed angle ⋮ Hyperbolicity of Varieties of Log General Type ⋮ The Uniformity Conjecture in Additive Combinatorics

Cites Work

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• There are integral heptagons, no three points on a line, no four on a circle
• Finiteness theorems for abelian varieties over number fields.
• Uniformity of stably integral points on elliptic curves
• Correlation for surfaces of general type
• A solution of the Erdős-Ulam problem on rational distance sets assuming the Bombieri-Lang conjecture
• Uniformity of rational points
• Integral distances

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