A modular interpretation of various cubic towers

Abstract

In this article we give a Drinfeld modular interpretation for various towers of function fields meeting Zink's bound

A survey on recursive towers and Ihara's constant

“…More is said in [7] about equation (11) and related equations. In [23], the key-ingredients from [7,1] were worked out further and used to give a precise modular description for each of the function fields in tower H. Considering Drinfeld modules as in D m,j , but in much greater generality, was used to obtain curves with many rational points over F q m in [36]. There the genus computation was carried out using very different techniques, more reminiscent to those in [35].…”

“…In particular, the tower over cubic finite fields from [19] and [10] then need a modular interpretation. A modular interpretation for various good towers over cubic finite fields was subsequently given in [1] using Drinfeld modules of rank three.…”

Good recursive towers over prime fields exist

“…The last one gives, under a unified construction, the best known lower bounds. The morphisms f and g resulting in good towers seem to be very special and in fact almost all have been proven to have a modular interpretation of various types (see [Elk98,Elk01,ABB17] among others).…”