  The goal of this contribution is to investigate L${}^2$ extension properties
for holomorphic sections of vector bundles satisfying weak semi-positivity
properties. Using techniques borrowed from recent proofs of the
Ohsawa-Takegoshi extension theorem, we obtain several new surjectivity results
for the restriction morphism to a non necessarily reduced subvariety, provided
the latter is defined as the zero variety of a multiplier ideal sheaf. These
extension results come with precise L${}^2$ estimates and (probably) optimal
curvature conditions.
