Effective Pila-Wilkie bounds for unrestricted Pfaffian surfaces

DOI10.1007/s00208-020-02029-xzbMath1485.03135arXiv1804.08232OpenAlexW3014432124MaRDI QIDQ2235231

Gareth O. Jones, Margaret E. M. Thomas

Publication date: 21 October 2021

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.08232

zbMATH Keywords

Pfaffian surfacePila-Wilkie bound

Mathematics Subject Classification ID

Rational points (14G05) Effectivity, complexity and computational aspects of algebraic geometry (14Q20) Model theory of ordered structures; o-minimality (03C64)

Related Items (2)

Wilkie's conjecture for Pfaffian structures ⋮ Torsion points with multiplicatively dependent coordinates on elliptic curves

Cites Work

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• Rational points in periodic analytic sets and the Manin-Mumford conjecture
• Volume growth and entropy
• \(C^ k\)-resolution of semialgebraic mappings, addendum to volume growth and entropy
• Frontier and closure of a semi-Pfaffian set
• Density of algebraic points on Noetherian varieties
• Complexity of stratifications of semi-Pfaffian sets
• Pfaffian definitions of Weierstrass elliptic functions
• On the algebraic points of a definable set
• Unlikely intersections in semiabelian surfaces
• Wilkie's conjecture for restricted elementary functions
• The rational points of a definable set
• Rational points on a subanalytic surface.
• Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181)
• THE DENSITY OF ALGEBRAIC POINTS ON CERTAIN PFAFFIAN SURFACES
• O-minimality and certain atypical intersections
• Relative Manin–Mumford for Semi-Abelian Surfaces
• Convergence results for function spaces over o-minimal structures
• Integer points on the dilation of a subanalytic surface
• A Manin–Mumford Theorem for the Maximal Compact Subgroup of a Universal Vectorial Extension of a Product of Elliptic Curves
• O-Minimality and Diophantine Geometry

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