  In this article we study certain asymptotic properties of global fields. We
consider the set of Tsfasman-Vladuts invariants of infinite global fields and
answer some natural questions arising from their work. In particular, we prove
the existence of infinite global fields having finitely many strictly positive
invariants at given places, and the existence of infinite number fields with
certain prescribed invariants being zero. We also give precisions on the
deficiency of infinite global fields and on the primes decomposition in those
fields.
