Maurer-Cartan spaces of filtered L-infinity algebras

We study several homotopical and geometric properties of Maurer-
Cartan spaces for L-infinity algebras which are not nilpotent, but only filtered in a
suitable way. Such algebras play a key role especially in the deformation
theory of algebraic structures. In particular, we prove that the Maurer-Cartan
simplicial set preserves fibrations and quasi-isomorphisms. Then we present an
algebraic geometry viewpoint on Maurer-Cartan moduli sets, and we compute
the tangent complex of the associated algebraic stack.