A G ] 2 2 Fe b 20 02 Schematic homotopy types and non-abelian Hodge theory I : The Hodge decomposition

In this work we use Hodge theoretic methods to study homotopy types of complex projective manifolds with arbitrary fundamental groups. The main tool we use is the schematization functor X → (X ⊗ C) sch , introduced by the third author as a substitute for the rationalization functor in homotopy theory in the case of non-simply connected spaces. Our main… CONTINUE READING