Séminaire de Mathématique

The Hochschild-Kostant-Rosenberg Theorem for Logarithmic Schemes, and Potential Applications for p-adic Hodge Theory

by Dmitry Vaintrob (IHES)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

I will give a definition of a certain category of "log quasicoherent" sheaves on a logarithmic variety which uses Falting's "almost mathematics" and which has the property that log differential forms and log polyvector fields are the Hochshild homology (appropriately understood) and Hochschild cohomology, respectively, of this category. This implies a certain "noncommutative Hodge theory" associated to a log variety in mixed characteristic. I will also explain (if there is time left over) a relationship of the proof of the main results to mirror symmetry.


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Ahmed Abbes