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• W3158889509 abstract "For any pair of orientable closed hyperbolic $3$--manifolds, this paper shows that any isomorphism between the profinite completions of their fundamental groups witnesses a bijective correspondence between the Zariski dense $mathrm{PSL}(2,mathbb{Q}^{mathtt{ac}})$--representations of their fundamental groups, up to conjugacy; moreover, corresponding pairs of representations have identical invariant trace fields and isomorphic invariant quaternion algebras. (Here, $mathbb{Q}^{mathtt{ac}}$ denotes an algebraic closure of $mathbb{Q}$.) Next, assuming the $p$--adic Borel regulator injectivity conjecture for number fields, this paper shows that uniform lattices in $mathrm{PSL}(2,mathbb{C})$ with isomorphic profinite completions have identical invariant trace fields, isomorphic invariant quaternion algebras, identical covolume, and identical arithmeticity." @default.
• W3158889509 created "2021-05-10" @default.
• W3158889509 creator A5008659449 @default.
• W3158889509 date "2021-05-03" @default.
• W3158889509 modified "2023-10-18" @default.
• W3158889509 title "Finite quotients, arithmetic invariants, and hyperbolic volume" @default.
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• W3158889509 doi "https://doi.org/10.48550/arxiv.2105.01022" @default.
• W3158889509 hasPublicationYear "2021" @default.
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