AI 中文总结
研究射影直线阿贝尔覆盖在特征$p$下的平凡性，通过计算与射影直线上乘法特征和相关的$L$函数的一般牛顿多边形，证明赫维茨空间的一般牛顿多边形与包含其像的最小志村簇的一致。
AI 中文摘要
我们证明，在特征$p$下，阶数与$p$互素的射影直线阿贝尔覆盖一般是$\mu$-平凡的。射影直线阿贝尔覆盖的赫维茨空间不可约分量在托雷利态射下的像位于某些志村簇中。这些簇按牛顿多边形分层已知，我们表明赫维茨空间的一般牛顿多边形与包含其像的最小志村簇的一般（或$\mu$-平凡）牛顿多边形一致。为此，我们计算了与射影直线上乘法特征和相关的$L$函数的一般牛顿多边形。
英文摘要
We show that abelian coverings of the projective line of order prime to $p$ are generically $μ$-ordinary in characteristic $p$. The images of the irreducible components of Hurwitz spaces of abelian coverings of the projective line by the Torelli morphism lie in some Shimura varieties. The stratification by Newton polygons of these varieties is known, and we show that the generic Newton polygon for the Hurwitz space coincides with the generic (or $μ$-ordinary) Newton polygon of the smallest Shimura variety that contains its image. In order to do this, we compute the generic Newton polygons for $L$-functions associated to multiplicative character sums over the projective line.
