In a 1966 paper (Rational surfaces over perfect fields, Publ. Math. IHES), Manin gave examples of cubic surfaces with Brauer group of order 2. In 1996, Urabe proved a conjecture of Tate on The bilinear form of the Brauer group of a surface (this is the title of his Invent. Math. 1996 paper) after noticing that Manin's examples, that were in contradiction with Tate's conjecture, were false (this he noted in Calculation of Manin's invariant for Del Pezzo surfaces, Math. of Computation 1996). Read a bit more on this story in Liu, Lorenzini, Raynaud, On the Brauer group of a surface, Invent. Math. 2005.
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