Let f be the finite field of order q2. It is sometimes attributed to Serre that any curve F-covered by the Hermitian curve Hq+1 : Yq+1 = xq + x is also F-maximal. For prime numbers q we show that every F-maximal curve X of genus g ≤ 2 with | Aut(X) | > 84(g - 1) is Galois-covered by Hq+1. The hypothesis on | Aut(X) | is sharp, since there exists an F-maximal curve X for q = 71 of genus g = 7 with | Aut(X) | = 84(7 - 1) which is not Galois-covered by the Hermitian curve H72.
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- Finite field
- Hermitian curve
- Maximal curve