In these lectures, we will present the analogy between function
fields of curves and  number fields from the point of view of
Arakelov theory. We will introduce Arakelov class groups and discuss
the relations between Arakelov divisors and ideal lattices. We will
mainly be interested in certain particular Arakelov divisors, called
reduced Arakelov divisors. This extends Shanks's definition of the
infrastructure of real quadratic fields to general number fields. We
will show that the finite set of reduced Arakelov divisors is, in a
precise sense, regularly distributed in the compact Arakelov class
group. 
  For more information see

http://www.mat.uniroma2.it/~schoof/14schoof.pdf

and the references there.