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

### Ya'acov Peterzil

University of Haifa, Israel### Sergei Starchenko

University of Notre Dame, USA

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## Abstract

In this short note we present an elementary proof of eorem 1.2 from [UY2], and also the Ax–Lindemann–Weierstrass theorem for abelian and semi-abelian varieties. The proof uses ideas of Pila, Ullmo, Yafaev, Zannier (see, e.g., [PZ]) and is based on basic properties of sets definable in o-minimal structures. It does not use the Pila–Wilkie counting theorem.

## Cite this article

Ya'acov Peterzil, Sergei Starchenko, A note on o-minimal flows and the Ax–Lindemann–Weierstrass theorem for semi-abelian varieties over $\mathbb C$. Enseign. Math. 63 (2017), no. 3, pp. 251–261

DOI 10.4171/LEM/63-3/4-1