The Galois closure of Drinfeld modular towers

Alp Bassa, Peter Beelen

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    In this article we study Drinfeld modular curves X0(pn) associated to congruence subgroups Γ0(pn) of GL(2,Fq[T]) where p is a prime of Fq[T]. For n>r>0 we compute the extension degrees and investigate the structure of the Galois closures of the covers X0(pn)→X0(pr) 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.
    Original languageEnglish
    JournalJournal of Number Theory
    Volume131
    Issue number3
    Pages (from-to)561-577
    ISSN0022-314X
    DOIs
    Publication statusPublished - 2011

    Keywords

    • Drinfeld modular curves
    • Galois closure
    • Asymptotically optimal towers of function fields

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