*Séminaire de Géométrie Algébrique de Rennes -
Exposé du 21 octobre 2005*

* *

**Daniel SCHEPLER ** (Rennes)

**Titre** :
Logarithmic nonabelian Hodge theory in characteristic p

**Résumé** :

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.

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