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arXiv · 2003.09027

Realizing Artin-Schreier covers of curves with minimal Newton polygons in positive characteristic

Jeremy Booher·Rachel Pries
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Abstract

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.

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Jeremy Booher, Rachel Pries. 2020-03-19. Realizing Artin-Schreier covers of curves with minimal Newton polygons in positive characteristic. https://arxiv.org/abs/2003.09027

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