Descent of the Definition Field of a Tower of Function Fields and Applications

2004/09/10 by Stephane Ballet, Ballet, Stephane, Dominique Le Brigand +3
Mathematics · #11G20 #14H25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G20 #msc:14H25

paper · pdf · doi:10.48550/arxiv.math/0409173

20 pages

arxiv created 2004/09/10 · arxiv updated 2009/12/01

Abstract

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 \F_q² to \F_q. 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.

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