The relative units-Picard complex and the Brauer group of a product
  We introduce the relative units-Picard complex of an arbitrary morphism of schemes and apply it to the problem of describing the (cohomological) Brauer group of a (fiber) product of schemes in terms of the Brauer groups of the factors. Under certain hypotheses, we obtain a five-term exact sequence involving the preceding groups which enables us to solve the indicated problem in the case of, e.g., (certain types of) ruled varieties over a field of characteristic zero. 
Cristian D. Gonzalez-Aviles
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