A Lindemann-Weierstrass theorem for semi-abelian varieties over function fields

Abstract

We prove an analogue of the Lindemann-Weierstrass theorem (that the exponentials of a Q \mathbb {Q} -linearly independent set of algebraic numbers are algebraically independent), replacing Q a l g \mathbb {Q}^{alg} by C ( t ) a l g \mathbb {C}(t)^{alg} and G m n \mathbb {G}_{m}^{n} by a semi-abelian variety over C ( t ) a l g \mathbb {C}(t)^{alg} . Both the formulations of our results and the methods are differential algebraic in nature.