Dirty or oxidizing, there is a big difference. If it is oxidizing, chances are that it is not clear coated, therefore, you will need a metal polish. Try polishing the platter's underside as a test before moving on to the top surface.
Good question. Without knowing more, I would just use a damp microfiber towel, rung out as far as it could go. You don't want to use any chemicals that could stain the finish. I don't know why the platter is getting dirty. Dusty perhaps, but dirty?
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