Abstract
Let
be an algebraically closed field of characteristic 0, and let
be a morphism of smooth projective varieties over the ring
of formal Laurent series. We prove that if a general geometric fiber of
is rationally connected, then the induced map
between the Berkovich analytifications of
and
is a homotopy equivalence. Two important consequences of this result are that the Berkovich analytification of any
-bundle over a smooth projective
-variety is homotopy equivalent to the Berkovich analytification of the base, and that the Berkovich analytification of a rationally connected smooth projective variety over
is contractible.
