Are division algebras over local fields compact mod center?

If D is a central division algebra over a local field F, is it true that $D^\times/F^\times$ is compact?

• According to lemma 2.2 of math.uni-bielefeld.de/~ccheng/Writings/modpJL.pdf, it is. – peter a g Jul 5 '17 at 14:53
• I am far from any books at the moment, but I would think - I'm not sure though - that Platonov and Rapinchuk would be a printed reference to check. – peter a g Jul 5 '17 at 17:05