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

Suppose X is a smooth projective connected curve defined over an algebraically closed field k of characteristic p > 0 and B subset of 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. (C) 2020 Elsevier Inc. All rights reserved.