Fix a positive integer g and a squarefree integer m. We prove the existence of a genus g curve \(C/{\mathbb {Q}}\) such that the mod m representation of its Jacobian is tame. The method is to analyse the period matrices of hyperelliptic Mumford curves, which could be of independent interest. As an application, we study the tame version of the inverse Galois problem for symplectic matrix groups over finite fields.

中文翻译：

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驯服扭转和驯服逆伽罗瓦问题

固定正整数g和无平方整数m。我们证明了属g曲线\（C / {\ mathbb {Q}} \）的存在，因此其Jacobian的mod m表示是驯服的。该方法是分析超椭圆Mumford曲线的周期矩阵，该矩阵可能是独立的。作为应用，我们研究有限域上辛矩阵群的逆Galois问题的驯服形式。