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arXiv · 1411.1140

A fake plane via 2-adic uniformization with torsion

Daniel Allcock·Fumiharu Kato
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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.

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Daniel Allcock, Fumiharu Kato. 2014-11-05. A fake plane via 2-adic uniformization with torsion. https://arxiv.org/abs/1411.1140

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