Let k be an algebraically closed field of characteristic p > 0. If g ≥ 3, there exist a k-curve C of genusg withAut(C) = {1} and a hyperelliptic k- curve D of genus g with Aut(D) approx= Z/2 (see e.g. [16] and [8], respectively). In this paper, we extend these results to curves with given genus and p-rank.rnIf C is a smooth projective k-curve of genus g with Jacobian Jac(C), then the p-rank of C is the integer fc such that the cardinality of Jac(C)[p](k) is p~(fc). It is known that 0 ≤ f_C≤ g. We prove the following result.
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机译：令k为特征p> 0的代数封闭场。如果g≥3，则存在Aus（C）= {1}的gensg的k曲线C和Aut（D）的g属的超椭圆k曲线D大约= Z / 2（分别参见例如[16]和[8]）。在本文中，我们将这些结果扩展到具有给定属和p-rank的曲线。rn如果C是具有Jacobian Jac（C）的g属的光滑投影k曲线，则C的p-rank为整数fc，使得Jac（C）[p]（k）的基数为p〜（fc）。已知0≤f_C≤g。我们证明以下结果。
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