Higher-rank extension conjecture for semisimple lattice cohomology

Let $G$ be a product of non-compact almost simple groups over local fields, or a connected semisimple Lie group with finite center and without compact factors, and let $\Gamma<G$ be an irreducible cocompact lattice. Theorems~ and~ assert the stated cohomology vanishing and comparison isomorphisms under property T. Higher-rank extension conjecture. These theorems hold for every semisimple group of higher rank, with or without property T. This would remove property T from both lattice-cohomology results in higher rank; the source offers this as a conjectural extension and supplies no proof.