||A fake projective plane via 2-adic uniformization with torsion
A fake projective plane via 2-adic uniformization with torsion
加藤, 文元 ,
Kato, FumiharuAllcock, Daniel
Tohoku mathematical journal
237 , 2017-06
We adapt the theory of non-Archimedean uniformization to construct a smooth surface from a lattice in PGL3Q2 that has nontrivial torsion. It turns out to be a fake projective plane, commensurable with Mumford's fake projective 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.