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The main purpose of this paper is to generalize the celebrated L${}^2$extension theorem of Ohsawa-Takegoshi in several directions : the holomorphicsections to extend are taken in a possibly singular hermitian line bundle, thesubvariety from which the extension is performed may be non reduced, theambient manifold is K{\"a}hler and holomorphically convex, but not necessarilycompact.

A general extension theorem for cohomology classes on non reduced analytic spaces