  I extend the definitions of schemes relative to monoids with zero - and
therefore, toric geometry - to the world of formal schemes. This expands the
usual framework to include, for instance, models for Mumford's degenerating
Abelian varieties.
  Following the usual toric paradigm, normal formal monoid schemes can be
classified in terms of certain cone complexes, and their properties understood
in combinatorial terms. I use this to give a simple algebraisation criterion.
  I also reformulate the traditional notions of separated and proper morphism
in a manner amenable to the context of relative formal geometry, and give
characterisations in terms of the topology of cone complexes.
