The purpose of this work is to prove the existence of an algebraic moduli classifying objects in a given triangulated category.

To any dg-category T (over some base ring k), we define a D−-stack MT in the sense of [TO�N B., VEZZOSI G., Homotopical algebraic geometry II: Geometric stacks and applications, Mem. Amer. Math. Soc., in press], classifying certain Top-dg-modules. When T is saturated, MT classifies compact objects in the triangulated category [T] associated to T. The main result of this work states that under certain finiteness conditions on T (eg if it is saturated) the D−-stack MT is locally geometric (ie union of open and geometric sub-stacks). As a consequence we prove the algebraicity of the group of auto-equivalences of saturated dg-categories. We also obtain the existence of reasonable moduli for perfect complexes on a smooth and proper scheme, as well as complexes of representations of a finite quiver.� 2007 Published by Elsevier Masson SAS