论文标题
以最小的牛顿多边形的曲线实现Artin-Schreier封面
Realizing Artin-Schreier covers of curves with minimal Newton polygons in positive characteristic
论文作者
论文摘要
假设$ x $是在代数封闭的特征$ p> 0 $和$ b \ subset x（k）$的代数封闭字段$ k $上定义的平稳的投影连接曲线，这是有限的，可能是空的点。 $ p $ p $ galois封面的牛顿多边形$ x $带有分支机构$ b $，取决于封面的后果不变。当$ x $是普通的时，对于每一套可能的分支点和分支不变的不变性，我们就会证明存在这样的封面，其牛顿多边形是最小或接近最小的封面。
Suppose $X$ is a smooth projective connected curve defined over an algebraically closed field $k$ of characteristic $p>0$ and $B \subset X(k)$ is a finite, possibly empty, set of points. The Newton polygon of a degree $p$ Galois cover of $X$ with branch locus $B$ depends on the ramification invariants of the cover. When $X$ is ordinary, for every possible set of branch points and ramification invariants, we prove that there exists such a cover whose Newton polygon is minimal or close to minimal.
