Rational points in periodic analytic sets and the Manin-Mumford conjecture

DOI10.4171/RLM/514zbMath1164.11029arXiv0802.4016WikidataQ123357172 ScholiaQ123357172MaRDI QIDQ931361

Publication date: 25 June 2008

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.4016

zbMATH Keywords

Conjecture of Manin-Mumford Rational points on analytic varieties Torsion points on algebraic varieties

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Analytic theory of abelian varieties; abelian integrals and differentials (14K20) Results involving abelian varieties (11J95)

Related Items (54)

Collinear CM-points ⋮ A note on o-minimal flows and the Ax-Lindemann-Weierstrass theorem for semi-abelian varieties over \(\mathbb{C}\) ⋮ About the mixed André-Oort conjecture: reduction to a lower bound for the pure case ⋮ The hyperbolic Ax-Lindemann-Weierstraß conjecture ⋮ Heights of pre-special points of Shimura varieties ⋮ Algebraic flows on abelian varieties ⋮ Unlikely intersections with Hecke translates of a special subvariety ⋮ Cyclotomic torsion points in elliptic schemes ⋮ Towards the André-Oort conjecture for mixed Shimura varieties: the Ax-Lindemann theorem and lower bounds for Galois orbits of special points ⋮ Torsion points on isogenous abelian varieties ⋮ The Manin-Mumford conjecture and the Tate-Voloch conjecture for a product of Siegel moduli spaces ⋮ The space of homogeneous probability measures on \(\overline{\Gamma \backslash X}^S_{\max}\) is compact (with an appendix by Jialun Li) ⋮ A nonarchimedean Ax-Lindemann theorem ⋮ On a conjecture of Buium and Poonen ⋮ An overview on problems of unlikely intersections in families of abelian varieties ⋮ Tameness in geometry and arithmetic: beyond o-minimality ⋮ Hodge theory, between algebraicity and transcendence ⋮ On the distribution of the Hodge locus ⋮ Multiplicative structures and random walks in o-minimal groups ⋮ \(o\)-minimality and the André-Oort conjecture for \(\mathbb{C}^{n}\) ⋮ An effective result of André-Oort type ⋮ Hyperbolic Ax-Lindemann theorem in the cocompact case ⋮ Algebraic flows on commutative complex Lie groups ⋮ Ax-Lindemann-Weierstrass with derivatives and the genus 0 Fuchsian groups ⋮ Ax-Lindemann for \(\mathcal{A}_g\) ⋮ The six Grothendieck operations on o-minimal sheaves ⋮ Torsion points with multiplicatively dependent coordinates on elliptic curves ⋮ Torsion anomalous points and families of elliptic curves ⋮ Torsion points on families of products of elliptic curves ⋮ Equations with powers of singular moduli ⋮ Torsion points on families of squares of elliptic curves ⋮ Heights in families of abelian varieties and the geometric Bogomolov conjecture ⋮ Density of algebraic points on Noetherian varieties ⋮ Rational products of singular moduli ⋮ Effective Pila-Wilkie bounds for unrestricted Pfaffian surfaces ⋮ Diophantine approximations on definable sets ⋮ On a modular Fermat equation ⋮ Product formulas for periods of CM abelian varieties and the function field analog ⋮ Effective André-Oort conjecture for non-compact curves in Hilbert modular varieties ⋮ Rational points on Grassmannians and unlikely intersections in tori ⋮ Zariski closures of images of algebraic subsets under the uniformization map on finite-volume quotients of the complex unit ball ⋮ Effective estimates for the degrees of maximal special subvarieties ⋮ Unlikely intersections between isogeny orbits and curves ⋮ Impossible intersections in a Weierstrass family of elliptic curves ⋮ CM RELATIONS IN FIBERED POWERS OF ELLIPTIC FAMILIES ⋮ Ax-Schanuel type theorems on functional transcendence via Nevanlinna theory ⋮ Complex cellular structures ⋮ Counting special points: Logic, diophantine geometry, and transcendence theory ⋮ An o-minimal characterization of special subvarieties ⋮ A note on divisible points of curves ⋮ Some unlikely intersections beyond André–Oort ⋮ Geometric and o-minimal Littlewood-Offord problems ⋮ Applications du théorème d’Ax–Lindemann hyperbolique ⋮ A short note on Manin–Mumford

Cites Work

This page was built for publication: Rational points in periodic analytic sets and the Manin-Mumford conjecture