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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 06 Dec 2023 14:28:08 +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-vhb23Arithmetic Quotients of the Complex Ball and a Conjecture of Lang
https://resolver.caltech.edu/CaltechAUTHORS:20160108-082533307
Authors: Dimitrov, Mladen; Ramakrishnan, Dinakar
Year: 2015
DOI: 10.48550/arXiv.1401.1628
We prove that various arithmetic quotients of the unit ball in C^n are Mordellic, in the sense that they have only finitely many rational points over any finitely generated field extension of Q. In the previously known case of compact hyperbolic complex surfaces, we give a new proof using their Albanese in conjunction with some key results of Faltings, but without appealing to the Shafarevich conjecture. In higher dimension, our methods allow us to solve an alternative of Ullmo and Yafaev. Our strongest result uses in addition Rogawski's theory and establishes the Mordellicity of the Baily-Borel compactifications of Picard modular surfaces of some precise levels related to the discriminant of the imaginary quadratic fields.https://authors.library.caltech.edu/records/eycp5-0fg25