
TL;DR
This paper classifies normal p-adic origamis, which are coverings of Mumford curves with at most one branch point, and explores their invariants and geometric structures in the p-adic setting.
Contribution
It provides a complete classification of all normal non-trivial p-adic origamis and relates them to square-gluing constructions in the p-adic context.
Findings
Classification of all normal non-trivial p-adic origamis
Calculation of invariants for these origamis
Description of p-adic origamis via square-gluing methods
Abstract
An origami (also known as square-tiled surface) is a Riemann surface covering a torus with at most one branch point. Lifting two generators of the fundamental group of the punctured torus decomposes the surface into finitely many unit squares. By varying the complex structure of the torus one obtains easily accessible examples of Teichm\"uller curves in the moduli space of Riemann surfaces. The p-adic analogues of Riemann surfaces are Mumford curves. A p-adic origami is defined as a covering of Mumford curves with at most one branch point, where the bottom curve has genus one. A classification of all normal non-trivial p-adic origamis is presented and used to calculate some invariants. These can be used to describe p-adic origamis in terms of glueing squares.
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.
