Algebraic and topological aspects of the schematization functor

L. Katzarkov, T. Pantev, B. Toën

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We study some basic properties of schematic homotopy types and the schematization functor. We describe two different algebraic models for schematic homotopy types, namely cosimplicial Hopf alegbras and equivariant cosimplicial algebras, and provide explicit constructions of the schematization functor for each of these models. We also investigate some standard properties of the schematization functor that are helpful for describing the schematization of smooth projective complex varieties. In a companion paper, these results are used in the construction of a non-abelian Hodge structure on the schematic homotopy type of a smooth projective variety.

Original languageEnglish (US)
Pages (from-to)633-686
Number of pages54
JournalCompositio Mathematica
Issue number3
StatePublished - May 2009


  • homotopy theory
  • non-abelian Hodge theory
  • schematic homotopy types

ASJC Scopus subject areas

  • Algebra and Number Theory


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