Uniqueness of Motivic Fargues-Fontaine Cohomology

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 show the uniqueness of such vector bundles, which, in particular, yields comparison theorems for them. Moreover, we show that one can choose a canonical comparison isomorphism between these vector bundles.