In this talk we will consider the question of how many rational points a curve over a finite field of large genus can have. For this purpose we will introduce towers of function fields. Several explicit examples of such towers with good asymptotic properties have been given by Garcia, Stichtenoth and others, and a modular interpretation for these was provided by Elkies. We will elaborate further on this modular interpretation and show how it can be used to obtain more insight in explicit optimal towers and to find new examples. We end up with some new results and a conjecture on the value of Iharas quantity A(q) for all nonprime values of the cardinality q of the finite field. This is joint work with Peter Beelen, Arnaldo Garcia and Henning Stichtenoth.
Freitag, den 4. Februar 2011 um 14:15 Uhr, in INF 288, HS 3 Freitag, den 4. Februar 2011 at 14:15, in INF 288, HS 3