  Even if a noninteracting system has zero Berry curvature everywhere in the
Brillouin zone, it is possible to introduce interactions that stabilise a
fractional Chern insulator. These interactions necessarily break time-reversal
symmetry (either spontaneously or explicitly) and have the effect of altering
the underlying band structure. We outline a number of ways in which this may be
achieved, and show how similar interactions may also be used to create a
(time-reversal symmetric) fractional topological insulator. While our approach
is rigorous in the limit of long range interactions, we show numerically that
even for short range interactions a fractional Chern insulator can be
stabilised in a band with zero Berry curvature.
