{"id":"openai-math/Arithmeticity-of-twisted-finite-correspondences-for-lattices-over-local-fields","pdf":"https://github.com/openai/math/blob/main/preprints/Arithmeticity-of-twisted-finite-correspondences-for-lattices-over-local-fields-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Arithmeticity-of-twisted-finite-correspondences-for-lattices-over-local-fields-September-23-2026","tags":["group-theory","lattices","rigidity","local-fields"],"score":0,"title":"Arithmeticity of twisted finite correspondences for lattices over local fields","domain":"Operator algebras","family":"286","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.OA","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Rigidity and arithmetic of lattice von Neumann algebras"}