The Galois closure of Drinfeld modular towers |
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Authors: | Alp Bassa |
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Institution: | a CWI, Amsterdam, The Netherlands b Technical University of Denmark, Department of Mathematics, Denmark |
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Abstract: | In this article we study Drinfeld modular curves X0(pn) associated to congruence subgroups Γ0(pn) of GL(2,FqT]) where p is a prime of FqT]. 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. |
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Keywords: | Drinfeld modular curves Galois closure Asymptotically optimal towers of function fields |
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