Séminaire de Géométrie Algébrique de Rennes - Exposé du 21 octobre 2005
Daniel SCHEPLER (Rennes)
Titre : Logarithmic nonabelian Hodge theory in characteristic p
The classical Cartier descent theorem requires that a connection have vanishing p-curvature to work; furthermore, it does not work for connections with log poles in general unless the residue of the connection also vanishes. I will present an extension of this theorem which does work on log schemes and also applies to more general connections for which the p-curvature only needs to satisfy a certain nilpotence condition.