The relative units-Picard complex and the Brauer group of a product
Abstract
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.
Cite
@article{arxiv.1606.04392,
title = {The relative units-Picard complex and the Brauer group of a product},
author = {Cristian D. Gonzalez-Aviles},
journal= {arXiv preprint arXiv:1606.04392},
year = {2017}
}
Comments
New title and several changes to the Introduction and to Section 4. Many thanks to the referee for noticing that my original rationality hypotheses could be considerably relaxed in the case of smooth and projective varieties. As a consequence, now several of my results also apply, for example, to certain pairs of abelian varieties. arXiv admin note: text overlap with arXiv:1604.04916