Ahmed Abbes - The p-adic Simpson correspondence: Functoriality by proper direct image and Hodge-Tate local systems

Collection Ahmed Abbes - The p-adic Simpson correspondence: Functoriality by proper direct image and Hodge-Tate local systems

Organizer(s) Ahmed Abbes (CNRS & IHÉS), Ana Caraiani (Imperial College London ), Ariane Mézard (Sorbonne Université), Takeshi Saito (University of Tokyo), Takeshi Tsuji (The University of Tokyo), Daxin Xu (Chinese Academy of Sciences), Weizhe Zheng (Chinese Academy of Sciences).
Date(s) 5/31/22 - 6/1/22
linked URL https://www.ihes.fr/~abbes/Luminy/luminy2022.html
00:00:00 / 00:00:00
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The p-adic Simpson correspondence: Functoriality by proper direct image and Hodge-Tate local systems (2/3)

By Ahmed Abbes

Faltings initiated in 2005 a p-adic analogue of the (complex) Simpson correspondence whose construction has been taken up by various authors and whose properties have been developed according to several approaches. I will present in these lectures the approach I developed with Michel Gros, inspired by the Cartier transform of Ogus and Vologodsky, which is an analogue in characteristic p of Simpson correspondence. The p-adic Simpson correspondence can be considered as a categorification of the Hodge-Tate decomposition. I will present its construction for small generalized representations using a suitable period ring, establish its functoriality by proper direct image and discuss the link with Hodge-Tate local systems.

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