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

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.