A fake plane via 2-adic uniformization with torsion
Algebraic Geometry
2014-11-06 v1 Group Theory
Abstract
We adapt the theory of non-Archimedean uniformization to construct a smooth surface from a lattice in PGL3(Q2) that has nontrivial torsion. It turns out to be a fake projective plane, commensurable with Mumford's fake plane yet distinct from it and the other fake planes that arise from 2-adic uniformization by torsion-free groups. As part of the proof, and of independent interest, we compute the homotopy type of the Berkovich space of our plane.
Keywords
Cite
@article{arxiv.1411.1140,
title = {A fake plane via 2-adic uniformization with torsion},
author = {Daniel Allcock and Fumiharu Kato},
journal= {arXiv preprint arXiv:1411.1140},
year = {2014}
}
Comments
17 pages