2020/03/19 by Booher, Jeremy, Pries, Rachel
#11G20 #11M38 #14D15 #14H30 #14H40 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2003.09027
Suppose X is a smooth projective connected curve defined over an algebraically closed field k of characteristic p>0 and B ⊂ 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.