de Mathématiques de Luminy
Ballet Stéphane, Lebrigand 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 from Fq2 to . 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.
2000 Mathematics Subject Classification: 11G20, 14H25.