  Given a proper morphism X -> S, we show that a large class of objects in the
derived category of X naturally form an Artin stack locally of finite
presentation over S. This class includes S-flat coherent sheaves and, more
generally, contains the collection of all S-flat objects which can appear in
the heart of a reasonable sheaf of t-structures on X. In this sense, this is
the Mother of all Moduli Spaces (of sheaves). The proof proceeds by studying
the finite presentation properties, deformation theory, and Grothendieck
existence theorem for objects in the derived category, and then applying
Artin's representability theorem.
