Period Spaces for p-divisible Groups

In this monograph p -adic period domains are associated to arbitrary reductive groups. Using the concept of rigid-analytic period maps the relation of p -adic period domains to moduli space of p -divisible groups is investigated. In addition, non-archimedean uniformization theorems for general Shimura varieties are established. The exposition includes background material on Grothendieck's "mysterious functor" (Fontaine theory), on moduli problems of p -divisible groups, on rigid analytic spaces,