  In [BM14b], the first author and Macr\`i constructed a family of nef divisors
on any moduli space of Bridgeland-stable objects on a smooth projective variety
X. In this article, we extend this construction to the setting of any separated
scheme Y of finite type over a field, where we consider moduli spaces of
Bridgeland-stable objects on Y with compact support. We also show that the nef
divisor is compatible with the polarising ample line bundle coming from the GIT
construction of the moduli space in the special case when Y admits a tilting
bundle and the stability condition arises from a \theta-stability condition for
the endomorphism algebra.
  Our main tool generalises the work of Abramovich--Polishchuk [AP06] and
Polishchuk [Pol07]: given a t-structure on the derived category D_c(Y) on Y of
objects with compact support and a base scheme S, we construct a constant
family of t-structures on a category of objects on YxS with compact support
relative to S.
