The Galois closure of Drinfeld modular towers

Publication: Research - peer-reviewJournal article – Annual report year: 2011

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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
Publication date2011
Volume131
Journal number3
Pages561-577
ISSN0022314x
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 0

Keywords

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