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

DOI10.1016/J.JNT.2020.04.010zbMATH Open1468.11144arXiv2003.09027OpenAlexW3027589721MaRDI QIDQ2187127

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Publication date: 2 June 2020

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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 $BsubsetX(k)$ 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.

Full work available at URL: https://arxiv.org/abs/2003.09027

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