Conference "Arithmetic, Geometry and Coding Theory"

March 14 - 18, 2011

CIRM, Marseille, France

Organisers: Yves Aubry (Université de la Méditerranée, IML), Christophe Ritzenthaler (Université de la Méditerranée, IML), Alexey Zykin (Mathematical Department of HSE, Laboratoire Poncelet, IITP)

Two families of maximal curves which are not Galois subcovers of the Hermitian curve

Kit-Ho Mak

Abstract

We show that the generalized Giulietti-Korchmaros curve (GK curve) and the maximal curve with equation x^{q^2}-x = y^{(q^n+1)/(q+1)} defined over the finite field of q^{2n} elements, for n \geq 3 odd and q \geq 3, are not Galois subcovers of the Hermitian curve over the same finite field. For q = 2, we show that the generalized GK curve is covered by the Hermitian curve. This is joint work with Iwan Duursma.

Web page of the conference at CIRM