2003/09/23 by Leonardo Zapponi, Zapponi, Leonardo
Engineering · Mathematics · #14 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:14
paper · pdf · doi:10.48550/arxiv.math/0309386
19 pages
arxiv created 2003/09/23 · openalex publication_date 2003/09/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let k be an algebraically closed field of positive characteristic. The goal of this paper is to characterize the proper smooth curves X/k of positive genus g equipped with a k-rational point P such that X¶can be realized as an etale cover of the affine line. A first elementary analysis shows that such a cover exists if and only if there exists an exact regular differential form on X having a unique zero at P (of order 2g-2). The main inconvenient of this approach is that it doesn't give any control on the degree of the cover. A finer investigation, essentially based on the duality between the Cartier operator and the Frobenius map allows to overcome this problem.