A recursive tower of function fields over F2

Official URL: http://risc01.sabanciuniv.edu/record=b1427165 (Table of Contents)

In 1995 Garcia and Stichtenoth gave explicit constructions of sequences of function fields over the finite eld Fq. Moreover, in the case that q = p^k (for k > 1 and p is a prime) they have given some examples of towers having positive limit. The problem is how to construct towers of function fields over the prime fields Fp with positive limit. In this thesis we give an example of recursive towers F = (F_0, F_1, ...) of function elds over the finite field F_2. In this example all steps Fi+1/Fi are Artin-Schreier extensions. Although we cannot determine whether the limit of the tower F is positive or not, we give some asymptotics for the genus and the number of rational places in this tower.