We use a certain sheaf of associative rings to define a global Ext functor. We prove that the "cohomologie totale" which we defined in an earlier paper in an analytic way is given by this global Ext. We use this functorial definition to prove some results conjectured in earlier papers. We introduce the "anchor spectral sequence" and use it to give a precise description of the total cohomology for the special case of complex homogeneous spaces.
Homology, Homotopy and Applications, Vol. 12 (2010), No. 1, pp.367-400.
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