"Wind from Rio, VI"

ABSTRACT: Maximal curves are the ones attaining the famous Hasse-Weil upper bound for the number of rational points on curves over finite fields (Riemann Hypothesis in this context). Ihara has shown that the genus of a maximal curve is upper bounded and it is well-known that the Hermitian curve is a maximal curve with the biggest genus possible (i.e., its genus attains the upper bound from Ihara). Serre has pointed out that subcovers of maximal curves are again maximal, and in particular we get that subcovers of the Hermitian curve are maximal curves. The first example of a maximal curve proven to be not a subcover of the Hermitian curve was found recently by Giulietti and Korchmaros. We present a generalization (and also a simplification) of their maximal curve. Joint work with Guneri and Stichtenoth.