Hochschild-Serre Statement for the total cohomology

Let M be a complex manifold and F a OM-module with a gholomorphic action where g is a complex Lie algebra (cf. [3]). We denote by H(g,F) the “total cohomology” as defined in [1] [2]. Then we prove that, for any ideal a ⊂ g ,t he moduleH • (a,F) viewed as a g/a-module, we have a spectral sequence which converges to H(g,F) and whose E2-term is E p,q 2 = H