de Mathématiques de Luminy
Ballet Stéphane, Le Brigand Dominique, Rolland Robert.
Descent of the definition field of a tower of function fields and applications.
Let us consider an algebraic function field defined over a finite Galois extension K of a perfect field k. We give some conditions allowing the descent of the definition field of the algebraic function field from K to k. We apply these results to the descent of the definition field of a tower of function fields. We give explicitly the equations of the intermediate steps of an Artin-Schreier type extension reduced fromto. By applying these results to a completed Garcia-Stichtenoth’s tower we improve the upper bounds and the upper asymptotic bounds of the bilinear complexity of the multiplication in finite fields.