Model theory and diophantine geometry

DOI10.1090/S0273-0979-97-00730-1zbMath0884.03040MaRDI QIDQ4372628

Anand Pillay

Publication date: 16 December 1997

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

zbMATH Keywords

Abelian varietyManin-Mumford conjectureMordell-Lang conjecturedifferentially closed fieldZariski set

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Rational points (14G05) Abelian varieties of dimension (> 1) (11G10) Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations (03-02)

Related Items (5)

Unnamed Item ⋮ Algebraization, transcendence, and \(D\)-group schemes ⋮ Bezout-type theorems for differential fields ⋮ Diophantine Geometry from Model Theory ⋮ Examples of torsion points on genus two curves

Cites Work

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• Elimination of quantifiers in algebraic structures
• Manin's proof of the Mordell conjecture over function fields
• Finiteness theorems for abelian varieties over number fields.
• Autour d'une conjecture de Serge Lang. (Around a conjecture by Serge Lang)
• The classification of the semisimple differential algebraic groups and the linear semisimple differential algebraic Lie algebras
• Number theory III: Diophantine geometry
• Differential algebraic groups of finite dimension
• Effective bound for the geometric Lang conjecture
• A gap theorem for abelian varieties over differential fields
• Division points on semi-abelian varieties
• Intersections in jet spaces and a conjecture of S. Lang
• Division points on curves
• A Note on Manin's Theorem of the Kernel
• Model theory of difference fields
• Groups and Fields Interpretable in Separably Closed Fields
• Uniform bound for generic points of curves in tori.
• Zariski geometries
• Rational points of algebraic curves over function fields
• The Mordell-Lang conjecture for function fields

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