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

Sergei Starchenko; Ya'acov Peterzil

arxiv: 1611.04673 · v1 · pith:GOEWADXHnew · submitted 2016-11-15 · 🧮 math.LO · math.NT

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

Ya'acov Peterzil , Sergei Starchenko This is my paper

classification 🧮 math.LO math.NT

keywords theoremabeliannoteo-minimalproofvarietiesax--lindemann--weierstrassax-lindemann-weierstrass

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In this short note we present an elementary proof of the Ax-Lindemann-Weierstrass theorem for abelian and semi-abelian varieties. The proof uses ideas of Pila, Ullmo, Yafaev, Zannier and is based on basic properties of sets definable in o-minimal structures. It does not use the Pila-Wilkie counting theorem.

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

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