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⊂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. Wh...

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Bibliographic Details
Published inJournal of number theory Vol. 214; pp. 240 - 250
Main Authors Booher, Jeremy, Pries, Rachel
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2020
Subjects
Artin-Schreier cover
Curve
Exponential sums
Formal patching
Jacobian
Newton polygon
p-rank
Positive characteristic
Wild ramification
Zeta function
secondary
Newton polygon
Wild ramification
Formal patching
p-rank
Curve
Zeta function
Jacobian
Positive characteristic
Artin-Schreier cover
Exponential sums
primary
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Summary: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.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2020.04.010