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 in:Journal of number theory 2020-09, Vol.214, p.240-250
Main Authors: Booher, Jeremy, Pries, Rachel
Format: Article
Language:English
Subjects:
Artin-Schreier cover
Curve
Exponential sums
Formal patching
Jacobian
Newton polygon
p-rank
Positive characteristic
Wild ramification
Zeta function
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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