  In this work we consider the question of realizing triangulated dg-categories
by derived categories of algebraic varieties. For this, we introduce the notion
of "system of points" in saturated dg-categories. We show that given such a
system on a dg-category T, we can construct an algebraic space M, of finite
type, smooth and separated, together with a dg-functor from T to a certain
twisted dg-category of sheaves on M. We prove that this functor is furthermore
an equivalence if and only if M is proper. All along this work we study
t-strutcures on algebraic families of objects in T, which might be of
independant interest.
