On the Brauer group of a product

Cristian D. Gonzalez-Aviles

Published 2016-06-14Version 1

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.