Séminaire TNGA : Kaixing Cao

Orateur : Kaixing Cao (Università degli Studi di Milano)

Titre : $p$-adic cohomology via the Fargues–Fontaine curve

Résumé : The discovery of the Fargues–Fontaine curve has led to major advances in the geometrization of $p$-adic Hodge theory. In this talk, we explain how several $p$-adic cohomology theories can be realized as vector bundles on the Fargues–Fontaine curve. We then present a motivic approach to comparing these vector bundles. As an application, we obtain comparison results between different $p$-adic cohomology theories for rigid analytic varieties.