相对单位-Picard 复形与乘积的 Brauer 群
代数几何
2017-05-15 v3 数论
摘要
我们引入了概形任意态射的相对单位-Picard 复形，并将其应用于描述概形（纤维）乘积的（上同调）Brauer 群用各因子的 Brauer 群表示的问题。在某些假设下，我们得到了一个涉及上述群的五项正合序列，这使我们能够解决例如特征为零的域上（特定类型的）直纹簇情况下的所述问题。
关键词
引用
@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}
}
备注
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