Séminaire de Mathématique

PD Higgs crystals and Higgs cohomology in characteristic p

by Prof. Takeshi TSUJI (Tokyo University & IHES)

Amphithéâtre Léon Motchane (Institut des Hautes Etudes Scientifiques)

Amphithéâtre Léon Motchane

Institut des Hautes Etudes Scientifiques

Bois-Marie 35, route de Chartres 91440 Bures-sur-Yvette
I will explain a recent work by Hidetoshi Oyama on a reformulation of the mod p analogue of the Simpson correspondence by Ogus and Vologodsky in terms of crystals on certain sites. He follows a similar work of the speaker on the p-adic Simpson correspondence by Faltings.
In the new formulation, the correspondence between D-modules and Higgs modules and the comparison between de Rham cohomology and Higgs cohomology are both given by the direct and inverse image functors of a certain morphism of topos.