A note on o-minimal flows and the Ax--Lindemann--Weierstrass theorem for   abelian varieties over $\mathbb{C}$
  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. 
Ya'acov Peterzil and Sergei Starchenko
math.LO math.NT