Diophantine Geometry from Model Theory

DOI10.2307/2687822zbMath0984.03035OpenAlexW2009526989MaRDI QIDQ2732528

Thomas J. Scanlon

Publication date: 5 May 2002

Published in: Bulletin of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/00cd62e0f2a57b8c0f9b1bac3614e59aaf4515bc

zbMATH Keywords

algebraic geometryManin-Mumford conjecturesocleprolongationsMordell-Lang conjecturepure fieldsdiophantine approximationsdiophantine geometryweakly normal groupsenriched fields

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Abelian varieties of dimension (> 1) (11G10)

Related Items (4)

Non-density of small points on divisors on Abelian varieties and the Bogomolov conjecture ⋮ Algebraic equations on the adelic closure of a Drinfeld module ⋮ Bezout-type theorems for differential fields ⋮ Approximation for Frobenius algebraic equations in Witt vectors

Cites Work

• A new strongly minimal set
• Finiteness theorems for abelian varieties over number fields.
• Mordell's conjecture over function fields
• Elimination of quantifiers for modules
• Model theory and algebraic geometry. An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture
• Difference algebraic subgroups of commutative algebraic groups over finite fields
• Einige Sätze über \(p\)-adische Potenzreihen mit Anwendung auf gewisse exponentielle Gleichungen
• Model theory and diophantine geometry
• Zariski geometries
• The Mordell-Lang conjecture for function fields

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