If D is a central division algebra over a local field F, is it true that $D^\times/F^\times$ is compact?
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According to lemma 2.2 of https://www.math.uni-bielefeld.de/~ccheng/Writings/modpJL.pdf, it is. – peter a g Jul 05 '17 at 14:53
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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 05 '17 at 17:05