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New maximal curves as ray class fields over Deligne-Lusztig curves


Author: Dane C. Skabelund
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 11G20; Secondary 14H25
DOI: https://doi.org/10.1090/proc/13753
Published electronically: August 30, 2017
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Abstract: We construct new covers of the Suzuki and Ree curves which are maximal with respect to the Hasse-Weil bound over suitable finite fields. These covers are analogues of the Giulietti-Korchmáros curve, which covers the Hermitian curve and is maximal over a base field extension. We show that the maximality of these curves implies that of certain ray class field extensions of each of the Deligne-Lusztig curves. Moreover, we show that the Giulietti-Korchmáros curve is equal to the above-mentioned ray class field extension of the Hermitian curve.


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Additional Information

Dane C. Skabelund
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Email: skabelu2@illinois.edu

DOI: https://doi.org/10.1090/proc/13753
Received by editor(s): June 29, 2016
Received by editor(s) in revised form: March 30, 2017
Published electronically: August 30, 2017
Communicated by: Romyar T. Sharifi
Article copyright: © Copyright 2017 American Mathematical Society