
TL;DR
This paper introduces Artin-Schreier root stacks to classify stacky curves in characteristic p, enabling direct incorporation of ramification data and facilitating computations of Riemann-Roch spaces and modular forms.
Contribution
It develops a new framework using Artin-Schreier root stacks to classify and analyze stacky curves with cyclic stabilizers in characteristic p, replacing traditional local structures.
Findings
Classified stacky curves with cyclic stabilizers using ramification data.
Computed dimensions of Riemann-Roch spaces for specific stacky curves.
Proposed a program for computing modular forms in positive characteristic.
Abstract
We classify stacky curves in characteristic with cyclic stabilizers of order 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
