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August 2022 Residually Finite Lattices in PU(2,1)˜ and Fundamental Groups of Smooth Projective Surfaces
Matthew Stover, Domingo Toledo
Michigan Math. J. 72: 559-597 (August 2022). DOI: 10.1307/mmj/20217215

Abstract

This paper studies residual finiteness of lattices in the universal cover of PU(2,1) and applications to the existence of smooth projective varieties with fundamental group a cocompact lattice in PU(2,1) or a finite covering of it. First, we prove that certain lattices in the universal cover of PU(2,1) are residually finite. To our knowledge, these are the first such examples. We then use residually finite central extensions of torsion-free lattices in PU(2,1) to construct smooth projective surfaces that are not birationally equivalent to a smooth compact ball quotient but whose fundamental group is a torsion-free cocompact lattice in PU(2,1).

Dedication

To Gopal Prasad in celebration of his 75th birthday

Citation

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Matthew Stover. Domingo Toledo. "Residually Finite Lattices in PU(2,1)˜ and Fundamental Groups of Smooth Projective Surfaces." Michigan Math. J. 72 559 - 597, August 2022. https://doi.org/10.1307/mmj/20217215

Information

Received: 26 May 2021; Revised: 20 December 2021; Published: August 2022
First available in Project Euclid: 2 August 2022

Digital Object Identifier: 10.1307/mmj/20217215

Subjects:
Primary: 14F35 , 20E26 , 22E40

Rights: Copyright © 2022 The University of Michigan

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Vol.72 • August 2022
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