Schematic homotopy types and non-abelian Hodge theory
Schematic homotopy types and non-abelian Hodge theory
Abstract 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 $X \mapsto (X\otimes \mathbb {C})^{\mathrm {sch}}$ , introduced by the third author as a substitute for the rationalization functor in homotopy theory in …