On Tsfasman-Vladuts Invariants of Infinite Global Fields

Philippe Lebacque (1)

1 UON - University of Nottingham, UK

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.

Mots clés: Infinite global fields; Tsfasman-Vladuts invariants; class field theory; class field towers; Grunwald-Wang theorem; Cebotarev density theorem

Domaines: Théorie des nombres [math.NT]

Philippe Lebacque. On Tsfasman-Vladuts Invariants of Infinite Global Fields. 2008. ⟨hal-00202502⟩