ELEMENTARY ABELIAN p-EXTENSIONS AND CURVES WITH MANY POINTS
By ´Alvaro Garzón Rojas Arnoldo Teheráan Herrera

Abstrac
In this paper we give a generalization of two results obtained by Garc´ıa and Stichtenoth ([G-S]) and use them to exhibit a method to construct curves over finite fields whose number of rational points is large compared to their genus. Such curves are induced by algebraic functions fields obtained from elementary abelian p-extensions of the rational function field Fq(x) using the trace operator T rFq/Fp Key words: Finite Fields, Algebraic Curves, Algebraic Function Fields, Elementary Abelian p-Extensions, Rational Points.
Resumen
En este articulo generalizamos dos resultados obtenidos por Garc´ıa & Stictenoth en ([G-S]) y usamos estas generalizaciones para construir curvas sobre cuerpos finitos cuyo n´umero de puntos racionales es grande en comparaci´on con su g´enero. Tales curvas son obtenidas considerando p extensiones abelianas elementales del cuerpo de funciones racionales Fq(x) usando el operador traza TrFq/Fp . Palabras clave: Cuerpos finitos, curvas algebraicas, cuerpos algebraicos de funciones, p−extensions abelianas elementales, puntos racionales.