Finite-Dimensional Continuous Quasirepresentations of Simple Adjoint Chevalley Groups over a Totally Disconnected Locally Compact Field

We prove that a simple adjoint Chevalley group over a totally disconnected field has no nontrivial pseudocharacters and no bounded nontrivial finite-dimensional quasirepresentations. Therefore, every finite-dimensional quasirepresentation with sufficiently small defect of this group is close to an ordinary representation of the group.