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Noncoherence of arithmetic hyperbolic lattices

Abstract

We prove that all arithmetic lattices in O (n, 1), n≥ 4, n ≠ 7, are noncoherent. We lso establish noncoherence of uniform arithmetic lattices of the simplest type in SU (2, 1), n ≥ 2, and of uniform lattices in SU(2, 1) which have infinite abelianization.

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