Semi-abelian analogues of Schanuel conjecture and applications

In this article we study semi-abelian analogues of Schanuel conjecture. As showed by the first author, conjecture is equivalent to Generalized Period applied 1-motives without abelian part. Extending her methods, second, third and fourth authors have introduced analogue as toric a result paper, define 1-motives. C. Cheng et al. proved that implies algebraic independence values iterated exponential logarithm, answering question M. Waldschmidt. The investigated similar in setup varieties: Weak Abelian an generalized logarithm. main paper Relative Semi-abelian