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arXiv · 1605.05428

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

Dane C. Skabelund
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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-Korchm\'aros 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-Korchm\'aros curve is equal to the above-mentioned ray class field extension of the Hermitian curve.

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Dane C. Skabelund. 2016-05-18. New maximal curves as ray class fields over Deligne-Lusztig curves. https://doi.org/10.1090/proc/13753

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