  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.

Algebraic Geometry;Number Theory