A simplified proof for the limit of a tower over a cubic finite field

Abstract

Recently Bezerra, Garcia and Stichtenoth constructed an explicit tower F = (Fn)n 0 of function fields over a finite field F q3 , whose limit λ(F) = limn→∞N(Fn)/g(Fn) attains the Zink bound λ(F) 2(q2 1)/(q + 2). Their proof is rather long and very technical. In this paper we replace the complex calculations in their work by structural arguments, thus giving a much simpler and shorter proof for the limit of the Bezerra, Garcia and Stichtenoth tower.