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

Stephane Ballet·Dominique Le Brigand·Robert Rolland
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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 $\F_{q^2}$ 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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Stephane Ballet, Dominique Le Brigand, Robert Rolland. 2004-09-10. Descent of the Definition Field of a Tower of Function Fields and Applications. https://arxiv.org/abs/math/0409173

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