Cyclic coverings of the projective line by Mumford curves in positive characteristic

2016/12/04 by Ryota Mikami, Mikami, Ryota
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1612.01077

20 pages, 2 figures, to appear in Kodai Mathematical Journal

openalex publication_date 2016/12/04 · openalex created_date 2016/12/16 · arxiv created 2017/07/15 · arxiv updated 2017/07/18 · openalex updated_date 2026/07/28

Abstract

We study the rigid analytic geometry of cyclic coverings of the projective line. We determine the defining equation of a cyclic covering of degree p of the projective line by a Mumford curve over a complete discrete valuation field of positive characteristic p. Previously, Bradley studied that of any degree over a non-archimedean local field of characteristic zero.

Related

• Cyclic p-groups and semi-stable reduction of curves in equal characteristic p>0
• Strongly Cyclic Coverings of Cyclic Curves
• a-Numbers of Cyclic Degree p² Covers of the Projective Line
• Mumford curves with maximal automorphism group
• On cyclic groups covers of the projective line