Schematic homotopy types and non-abelian Hodge theory

@article{Katzarkov2008SchematicHT,
  title={Schematic homotopy types and non-abelian Hodge theory},
  author={Ludmil Katzarkov and Tony Pantev and Bertrand Toen},
  journal={Compositio Mathematica},
  year={2008},
  volume={144},
  pages={582 - 632}
}
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 the case of non-simply connected spaces. Our main result is the construction of a Hodge decomposition on $(X\otimes \mathbb {C})^{\mathrm {sch}}$. This Hodge… Expand
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