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Decomposition theorem for proper Kähler morphisms

Introduction. In [S1], [S2] we introduced the notion of polarizable Hodge Modules on complex analytic spaces, which corresponds philosophically to that of pure perverse sheaves in characteristic p [BBD]. If X is smooth, MH(X,n)p the category of polarizable Hodge Modules of weight n (and with k-structure) is a full subcategory of the category of filtered holonomic •¬x-Modules (M,F) with k-structure by a given isomorphism ƒ¿ : DR(M)•¬C•¬k K for a perverse sheaf K (defined over k). Here k is a subfield of R, and we assume for simplicity k=R in this note. In general MH(X,n)p is defined using local embeddings into smooth varieties, and the underlying perverse sheaves K are