Relative p-adic Hodge theory and Rapoport-Zink period domains

TL;DR

This paper explores relative p-adic Hodge theory by constructing the universal admissible filtration of an isocrystal over a p-adic field extension, linking it to universal crystalline local systems.

Contribution

It introduces a novel construction of the universal admissible filtration and crystalline local systems within the framework of relative p-adic Hodge theory.

Findings

Construction of the universal admissible filtration for isocrystals.

Establishment of the associated universal crystalline local system.

Illustration of the theory through Rapoport-Zink period domains.

Abstract

As an example of relative p-adic Hodge theory, we sketch the construction of the universal admissible filtration of an isocrystal (\phi$-module) over the completion of the maximal unramified extension of Q_p, together with the associated universal crystalline local system.