Satake compactification of analytic Drinfeld modular varieties

We construct a normal projective rigid analytic compactification of an arbitrary Drinfeld modular variety whose boundary is stratified by varieties smaller dimensions. This generalizes work Kapranov. Using algebraic that Pink and Schieder's, we show the naturally isomorphic to analytification Pink's compactification. interpret forms as global sections natural ample invertible sheaves on deduce finiteness results for spaces such forms.