Artin-Schreier Root Stacks

2019/10/08 by Kobin, Andrew · 2 citations
#11S15 #14D23 #14Q05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1910.03146

Abstract

We classify stacky curves in characteristic p > 0 with cyclic stabilizers of order p using higher ramification data. This approach replaces the local root stack structure of a tame stacky curve, similar to the local structure of a complex orbifold curve, with a more sensitive structure called an Artin-Schreier root stack, allowing us to incorporate this ramification data directly into the stack. As an application, we compute dimensions of Riemann-Roch spaces for some examples of stacky curves in positive characteristic and suggest a program for computing spaces of modular forms in this setting.

Cited by

• Wild Stacky Curves and Rings of Mod p Modular Forms
• The integral Hasse principle for stacky curves associated to a family of generalized Fermat equations

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• Moduli of Curves of Genus One with Twisted Fields