Rigidity and arithmetic of lattice von Neumann algebras

Classifies finite-index bimodules between scalar-twisted group factors of ICC groups commensurable with property-$(T)$ lattices over characteristic-zero local fields and arbitrary ICC group factors. Every such bimodule is a summand of finite sums of models arising from finite-index subgroup isomorphisms and finite-dimensional projective representations. The classification also recovers the group, scalar cocycle and amplification scale up to the stated stable equivalence.