Algebraic and topological aspects of the schematization functor.

Ludmil Katzarkov , Tony Pantev , Bertrand Toen (1)

1 LEP - Laboratoire Émile Picard

We study some basic properties of schematic homotopy types and the schematization functor. We describe two different algebraic models for schematic homotopy types: co-simplicial Hopf alegbras and equivariant co-simplicial algebras, and provide explicit constructions of the schematization functor for each of these models. We also investigate some standard properties of the schematization functor helpful for the description of 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.

Domaines: Topologie algébrique [math.AT]; Géométrie algébrique [math.AG]

Ludmil Katzarkov, Tony Pantev, Bertrand Toen. Algebraic and topological aspects of the schematization functor.. Compositio Mathematica, 2009, 145 (03), pp.633-686. ⟨10.1112/S0010437X09004096⟩. ⟨hal-00772926⟩