On Tsfasman--Vl\u{a}du\c{t} Invariants of Infinite Global Fields

TL;DR

This paper investigates the asymptotic properties of infinite global fields through Tsfasman-Vladuts invariants, establishing existence results for fields with prescribed invariants and analyzing their deficiency and prime decomposition.

Contribution

It proves the existence of infinite global fields with finitely many positive invariants and fields with certain invariants zero, advancing understanding of their asymptotic behavior.

Findings

Existence of infinite global fields with finitely many positive invariants

Existence of fields with certain invariants equal to zero

Results on deficiency and prime decomposition in infinite global fields

Abstract

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.