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In 2017 Skabelund constructed two new examples of maximal curves S ˜ q and R ˜ q as covers of the Suzuki and Ree curves, respectively. The resulting Skabelund curves are analogous to the Giulietti–Korchmáros cover of the Hermitian curve. In this paper a complete characterization of all Galois subcovers of the Skabelund curves S ˜ q and R ˜ q is given. Calculating the genera of the corresponding curves, we find new additions to the list of known genera of maximal curves over finite fields. [ABSTRACT FROM AUTHOR]

Abstract: In this article we study Drinfeld modular curves associated to congruence subgroups of where p is a prime of . For we compute the extension degrees and investigate the structure of the Galois closures of the covers 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. [ABSTRACT FROM AUTHOR]