(joint work with G. Wüstholz)

1-periods are complex numbers obtained by integrating algebraic 1-forms over paths with end points in algebraic numbers (or more precisely, linear combinations of such). The set contains famous number like \pi or logarithms of algebraic numbers. They tend to be transcendental.

We will give a conceptual interpretation of all linear relations between these numbers in terms of 1-motives. This establishes the periods conjecture formulated by Kontsevich and Zagier in this case (but not Grothendieck's version that describes all algebraic relations).

Time permitting, we will also explain how to deduce dimension formulas for spaces of 1-periods from the qualitative result.