p-adic Hodge theory in motivic homotopy

Algebro-Geometric and Homotopical Methods

06 April 11:00 - 12:00

Frederic Deglise - Université de Bourgogne

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.
Eric M. Friedlander
University of Southern California
Lars Hesselholt
University of Copenhagen
Paul Arne Østvaer
University of Oslo


Paul Arne Østvaer


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