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2017 A fake projective plane via 2-adic uniformization with torsion
Daniel Allcock, Fumiharu Kato
Tohoku Math. J. (2) 69(2): 221-237 (2017). DOI: 10.2748/tmj/1498269624

Abstract

We adapt the theory of non-Archimedean uniformization to construct a smooth surface from a lattice in ${\rm PSL}_3(\mathbb{Q}_2)$ 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. "A fake projective plane via 2-adic uniformization with torsion." Tohoku Math. J. (2) 69 (2) 221 - 237, 2017. https://doi.org/10.2748/tmj/1498269624

Information

Published: 2017
First available in Project Euclid: 24 June 2017

zbMATH: 06775253
MathSciNet: MR3682164
Digital Object Identifier: 10.2748/tmj/1498269624

Subjects:
Primary: 11F23
Secondary: 14J25

Rights: Copyright © 2017 Tohoku University

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Vol.69 • No. 2 • 2017
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