Rational points on analytic varieties

DOI10.4171/EMSS/10zbMath1330.14031arXiv1408.1441OpenAlexW2963549730MaRDI QIDQ2352770

Alexey Beshenov, Margaret Bilu, Purusottam Rath, Yuri F. Bilu

Publication date: 6 July 2015

Published in: EMS Surveys in Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.1441

zbMATH Keywords

surveyrational pointso-minimalityManin-Mumford conjectureAndré-Oort conjecturedefinable setsanalytic varietiescounting pointsPila

Mathematics Subject Classification ID

Rational points (14G05) Arithmetic aspects of modular and Shimura varieties (11G18) Lattice points in specified regions (11P21) Results involving abelian varieties (11J95) Model theory of ordered structures; o-minimality (03C64)

Cites Work

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• Semianalytic and subanalytic sets
• The elementary theory of restricted analytic fields with exponentiation
• The density of rational points on curves and surfaces. (With an appendix by J.-L. Colliot-Thélène).
• Uniform definability of the Weierstrass \(\wp\) functions and generalized tori of dimension one
• Geometric categories and o-minimal structures
• Counting rational points on algebraic varieties
• Projections of semi-analytic sets
• The number of integral points on arcs and ovals
• A generalization of the Tarski-Seidenberg theorem, and some nondefinability results
• Exponential diophantine equations

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