Some Artin–Schreier towers are easy

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 Artin–Schreier towers. As an illustration of our method, we obtain a very simple and unified proof for the limits of some towers that attain the Drinfeld–Vlǎdut̨ bound or the Zink bound.