An equality between two towers over cubic fields

TL;DR

This paper reveals an equivalence between two towers of function fields over cubic fields, showing that removing the bottom field from one tower yields the same structure as a previously known tower.

Contribution

It demonstrates an unexpected equivalence between two different constructions of towers over cubic fields, clarifying their relationship.

Findings

Removing the bottom field from Bassa-Garcia-Stichtenoth tower yields the same tower as a known construction.

The equivalence simplifies understanding the structure of towers over cubic fields.

The result connects two previously separate approaches to tower construction.

Abstract

Recently Bassa, Garcia and Stichtenoth constructed a tower of function fields over GF(q^3) having many rational places relative to their genera. We show that, by removing the bottom field from this tower, we obtain the same tower we would obtain by removing certain fields from a tower constructed previously by Bezerra, Garcia and Stichtenoth.