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Frederic Deglise: p-adic Hodge theory in motivic homotopy

Tid: To 2017-04-06 kl 11.00 - 12.00

Plats: Institut Mittag-Leffler, Auravägen 17, Djursholm

Medverkande: Frederic Deglise, ENS de Lyon

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Abstract: I will present a work in progress in collaboration with Wiesia Niziol which aims to incorporate p-adic Hodge theory into the framework of modules over ring spectra, in the sense of Morel-Voevodsky's motivic homotopy theory. Our main result is the identification of "modules over syntomic cohomology" as a full subcategory of the derived category of potentially semi-stable representations, making use of ideas of Beilinson and Drew. I will then present an ongoing project to extend Fontaine semi-stable comparison to a suitable notion of syntomic modules. The later should be compared to Saito mixed Hodge modules, and our objective is to get some kind of p-adic Riemann-Hilbert correspondence.