Résume | In analogy to the complex Corlette-Simpson correspondence, p-adic non-abelian Hodge theory studies p-adic representations of fundamental groups of smooth projective varieties with the methods of p-adic Hodge theory. In this talk, I will first explain how v-vector bundles arise naturally in this context, and how we can relate these to Higgs bundles via the p-adic Simpson correspondence. I will then sketch how in joint work with Daxin Xu, we interpret the correspondence more geometrically as a twisted isomorphism between the moduli stacks of either side. |