Abstract :
The generalized Grothendieckʹs conjecture of periods (CPG)K predicts that if M is a 1-motive defined over an algebraically closed subfield K of image, then image. In this article we propose a conjecture of transcendance that we call the elliptico-toric conjecture (CET). Our main result is that (CET) is equivalent to (CPG)K applied to 1-motives defined over K of the kind image. (CET) implies some classical conjectures, as the Schanuelʹs conjecture or its elliptic analogue, but it implies new conjectures as well. All these conjectures following from (CET) are equivalent to (CPG)K applied to well chosed 1-motives: for example the Schanuelʹs conjecture is equivalent to (CPG)K applied to 1-motives of the kind image.
