Some Artin-Schreier towers are easy

Abstract

Towers of function fields (resp., of algebraic curves) with positive limit provide examples of curves with large genus having many rational points over a finite field. It is in general a difficult task to calculate the genus of a wild tower. In this paper, we present a method for calculating the genus of certain ArtinSchreier towers. As an illustration of our method, we obtain a very simple and unified proof for the limits of some towers that attain the DrinfeldVlăduţ bound or the Zink bound.