Let X be a cubic surface over a p-adic field k. Given an Azumaya algebra on X, we describe the local evaluation map X(k) → Q/Z in two cases, showing a sharp dependence on the geometry of the reduction of X. When X has good reduction, then the evaluation map is constant. When the reduction of X is a cone over a smooth cubic curve, then generically the evaluation map takes as many values as possible. We show that such a cubic surface defined over a number field has no Brauer-Manin obstruction. This extends results of Colliot-Thélène, Kanevsky and Sansuc.
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