Quelques r\'esultats effectifs concernant les invariants de Tsfasman-Vladuts

TL;DR

This paper investigates the properties of infinite algebraic extensions of global fields using Tsfasman-Vladuts invariants, employing recent results to construct fields with specific invariants and controlled deficiencies.

Contribution

It introduces methods to construct infinite global fields with prescribed invariants and zero invariants, advancing understanding of their decomposition properties.

Findings

Constructed infinite global fields with specified invariants.

Demonstrated control over invariants and deficiencies.

Extended previous results using recent theorems.

Abstract

We consider properties of infinite algebraic extensions of global fields through their Tsfasman-Vladuts invariants (related in particular to the decomposition of primes). We use recent results of A. Schmidt and a weak effective version of the Grunwald-Wang theorem to construct infinite global fields having at the same time a given finite set of positive invariants, a prescribed set of invariants being zero and a controlled deficiency.