The Hasse-Witt invariant in some towers of function fields over finite fields

摘要

In this article we investigate the p-rank of function fields in several good towers. To do this we first recall and establish some properties of the behaviour of the p-rank under extensions. Then we compute the p-ranks of function fields in several optimal towers over a quadratic field F_q2, as well as for a specific good tower over a cubic field F_q3, which was introduced by Bassa, Garcia and Stichtenoth.