Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 286-01. Arithmeticity of twisted finite correspondences for lattices over local fields
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OpenAI@2026-10-07#rem:oai-p-286-01
Authors: OpenAI. Family 286.
Title: Arithmeticity of twisted finite correspondences for lattices over local fields.
Abstract: We prove arithmetic exhaustion for bifinite correspondences between arbitrarily scalar-twisted group factors of ICC groups commensurable with property-$(T)$ lattices over characteristic-zero local fields and twisted group factors of arbitrary countable ICC groups. Every such correspondence is a closed summand of a finite direct sum of models obtained from actual finite-index subgroup isomorphisms and finite-dimensional projective representations of the matched cocycle ratio. The proof includes reducible products, mixed real and finite places, and quaternionic and Cayley rank-one factors.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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