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

JOURNAL OF NUMBER THEORY

卷:214

Article

Booher, Jeremy¹  Pries, Rachel² 

[1] Univ Canterbury, Sch Math & Stat, Christchurch 8140, New Zealand

[2] Colorado State Univ, Dept Math, Ft Collins, CO 80523 USA

关键词: Curve;    Jacobian;    Positive characteristic;    Artin-Schreier cover;    Wild ramification;    Zeta function;    Newton polygon;    Exponential sums;    p-rank;    Formal patching;   

DOI  :  10.1016/j.jnt.2020.04.010

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free