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Jun 13, 2010 at 18:58 comment added Charles Matthews en.wikipedia.org/wiki/Tsen%27s_theorem and references. The Brauer group is indeed trivial. I suppose this is proved in geometric analogues of class field theory.
Jun 13, 2010 at 18:52 comment added carlos Sorry, I meant L is a skew field. I fixed the mistake.
Jun 13, 2010 at 18:38 history answered Charles Matthews CC BY-SA 2.5