Examples of diamonds

Abstract

This chapter assesses some interesting examples of diamonds. So far, the only example encountered is the self-product of copies of Spd Qp. The chapter first studies this self-product. It is useful to keep in mind that a diamond can have multiple “incarnations.” Another important class of diamonds, which in fact were one of the primary motivations for their definition, is the category of Banach-Colmez spaces. Recently, le Bras has reworked their theory in terms of perfectoid spaces. The category of Banach-Colmez spaces over C is the thick abelian subcategory of the category of pro-étale sheaves of Qp-modules. This is similar to a category considered by Milne in characteristic p.