Global Fields

July 2 - 6, 2007, Moscow, Russia

Laboratoire J.-V. Poncelet

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Philippe Lebacque

Institut de Mathematiques de Luminy, France

On the Set of Tsfasman-Vladut invariants of infinite global fields

Tsfasman and Vl\u adu\c t defined the set of invariants $\{\phi_q, q \text{ is a prime power, } \mathbb{R} \text{ or }\mathbb{C}\}$ of infinite global fields, but the properties of this sets are still not known. For example, we do not know if infinitely many of these invariants can be non-zero, or if there is an asymptotically good infinite number field whose finite invariants are all zero. In this direction, I will talk about the constructions of infinite global fields having $n$ prescribed non-zero invariants, and of others having $n$ prescribed zero invariants.