论文标题
关于超ellip曲曲线的Galois表示
On Galois representations of superelliptic curves
论文作者
论文摘要
dvr $ {\ mathcal o} $剩余特性$ p $的超椭圆曲线是公式$ c：y^n = f（x）$的曲线。本文的目的是描述$ f（x）$在$ {\ mathcal o} $的分数字段和该$ p \ nmid n $的分数字段中，$ f（x）$都具有所有根源。我们的结果启发了[BW17]中给出的算法，但我们的描述是根据[DDMM18]中定义的群集图片给出的。
A superelliptic curve over a DVR ${\mathcal O}$ of residual characteristic $p$ is a curve given by an equation $C:y^n=f(x)$. The purpose of the present article is to describe the Galois representation attached to such a curve under the hypothesis that $f(x)$ has all its roots in the fraction field of ${\mathcal O}$ and that $p \nmid n$. Our results are inspired on the algorithm given in [BW17] but our description is given in terms of a cluster picture as defined in [DDMM18].
