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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 17:57:56 +0000Compact arithmetic quotients of the complex 2-ball and a conjecture of Lang
https://resolver.caltech.edu/CaltechAUTHORS:20140428-101450443
Authors: Dimitrov, Mladen; Ramakrishnan, Dinakar
Year: 2014
DOI: 10.48550/arXiv.1401.1628
Let X be a compact quotient of the unit ball in ℂ^2 by an arithmetic subgroup Γ of a unitary group defined by an anisotropic hermitian form on a three dimensional vector space over a CM field with signature (2,1) at one archimedean place and (3,0) at the others. We prove that if all the torsion elements of Γ are scalar, then X is Mordellic, meaning that for any number field k containing the field of definition of X, the set X(k) of k-rational points of X is finite. The proof applies and combines certain key results of Faltings with the work of Rogawski and the hyperbolicity of X.https://authors.library.caltech.edu/records/e67ha-vhb23