Brauer groups and Picard groups of affinoid p-adic spaces (Ref: 4342-6)

在这个项目中，Mark Heavy打算研究仿射p进曲线和仿射p进空间在p进局部域上的一般算法。他特别打算研究这些空间的Picard群和Brauer群，并确定它们作为群的结构。Mark还将研究在p进仿射曲线的情况下，Picard和Brauer群之间存在完美配对的可能性，并证明在这种情况下Brauer群是有限的。

In this project Mark Heavy intends to study the arithmetic of affinoid p-adic curves and affinoid p-adic spaces, in general, over p-adic local fields. He in particular intendes to study the Picard and Brauer groups of these spaces and determine their structure as groups. Mark will also investigate, in the case of p-adic affinoid curves, the possibility of the existence of a pefect pairing bewteen the Picard and the Brauer group and prove that the Brauer group in this case is finite.