The Galois closure of Drinfeld modular towers

JOURNAL OF NUMBER THEORY

卷:131

Article

Bassa, Alp²  Beelen, Peter¹ 

[1] Tech Univ Denmark, Dept Math, Copenhagen, Denmark

[2] CWI, NL-1009 AB Amsterdam, Netherlands

关键词: Drinfeld modular curves;    Galois closure;    Asymptotically optimal towers of function fields;   

DOI  :  10.1016/j.jnt.2010.10.006

来源: Elsevier

【 摘 要 】

In this article we study Drinfeld modular curves X(0)(p(n)) associated to congruence subgroups Gamma(0)(p(n)) of GL(2,F(q)[T]) where p is a prime of F(q)[T]. For n > r > 0 we compute the extension degrees and investigate the structure of the Galois closures of the covers X(0)(p(n)) -> X(0)(p(r)) and some of their variations. The results have some immediate implications for the Galois closures of two well-known optimal wild towers of function fields over finite fields introduced by Garcia and Stichtenoth, for which the modular interpretation was given by Elkies. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free