Fp2-MAXIMAL CURVES WITH MANY AUTOMORPHISMS ARE GALOIS-COVERED BY THE HERMITIAN CURVE
نویسندگان
چکیده
Let F be the finite field of order q, q = p with p prime. It is commonly atribute to J.P. Serre the fact that any curve F-covered by the Hermitian curve Hq+1 : y = x + x is also F-maximal. Nevertheless, the converse is not true as the GiuliettiKorchmáros example shows provided that q > 8 and h ≡ 0 (mod 3). In this paper, we show that if an F-maximal curve X of genus g ≥ 2 where q = p is such that |Aut(X )| > 84(g − 1) then X is Galois-covered by Hp+1. Also, we show that the hypothesis on the order of 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
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