A note on o-minimal flows and the Ax-Lindemann-Weierstrass theorem for semi-abelian varieties over \(\mathbb{C}\)

DOI10.4171/LEM/63-3/4-1zbMath1402.14060arXiv1611.04673OpenAlexW4237734947MaRDI QIDQ1624909

Sergei Starchenko, Yaa'cov Peterzil

Publication date: 16 November 2018

Published in: L'Enseignement Mathématique. 2e Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.04673

zbMATH Keywords

Ax-Lindemann-Weierstrass theoremo-minimal flow

Mathematics Subject Classification ID

Real-analytic and semi-analytic sets (14P15) Transcendence (general theory) (11J81) Subvarieties of abelian varieties (14K12) Applications of model theory (03C98) Model theory of ordered structures; o-minimality (03C64) Analytic subsets of affine space (32B15)

Related Items (4)

Big Picard theorem for jet differentials and non-Archimedean Ax-Lindemann theorem ⋮ Analytic Ax-Schanuel for semi-abelian varieties and Nevanlinna theory ⋮ Algebraic flows on commutative complex Lie groups ⋮ Lengths of developments in \(K((G))\)

Cites Work

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• The theory of the exponential differential equations of semiabelian varieties
• Courbes sur une variété abélienne et points de torsion
• On the real exponential field with restricted analytic functions
• Hyperbolic Ax-Lindemann theorem in the cocompact case
• Ax-Lindemann for \(\mathcal{A}_g\)
• The rational points of a definable set
• Some Basic Theorems on Algebraic Groups
• o-minimal Flows on Abelian Varieties
• Some Topics in Differential Algebraic Geometry I: Analytic Subgroups of Algebraic Groups
• Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function

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