On the Zeta function and the automorphism group of the generalized Suzuki curve

2019/12/03 by Borges, Herivelto, Coutinho, Mariana
#11G20 #14G05 #14G10 #14H37 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.01659

Abstract

For p an odd prime number, q₀=p^t, and q=p^2t-1, let X_G_S be the nonsingular model of Y^q-Y=X^q₀(X^q-X). In the present work, the number of \mathbbF_qⁿ-rational points and the full automorphism group of X_G_S are determined. In addition, the L-polynomial of this curve is provided, and the number of \mathbbF_qⁿ-rational points on the Jacobian J_X_G_S is used to construct étale covers of X_G_S, some with many rational points.

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