  We study here the Berkovich line over the ring of integers of a number field.
It is a natural object which contains complex and non-Archimedean analytic
spaces associated to each place. We prove that this line satisfies good
topological and algebraic properties and exhibit a few examples of Stein spaces
that lie in it. We derive applications to the study of convergent arithmetic
power series: choice of zeroes and poles, noetherianity of global rings and
inverse Galois problem. Typical examples of such power series are given by
analytic functions on the open complex unit disk whose Taylor development in 0
has integer coefficients.
