  We set up the geometric background necessary to extend rigid cohomology from
the case of algebraic varieties to the case of general locally noetherian
formal schemes. In particular, we generalize Berthelot's strong fibration
theorem to adic spaces: we show that if we are given a morphism of locally
noetherian formal schemes which is partially proper and formally smooth around
a formal subscheme, and we pull back along a morphism from an analytic space
which is locally of noetherian type, then we obtain locally a fibration on
strict neighborhoods.
