  Let F be a global field, and let S be a finite set of places of F containing
all archimedean places. Consider the product X of the symmetric spaces and
Bruhat-Tits buildings for PGL_d of the completions of F at archimedean and
non-archimedean places in S, respectively. We construct compactifications of
the quotient of X by S-arithmetic subgroups of PGL_d(F). The constructions make
delicate use of reductive Borel-Serre spaces for archimedean places and
polyhedral and seminorm compactifications at nonarchimedean places. We also
briefly discuss a few potential applications of our compacifications.
