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

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.Comment: 20 page

Semistable reduction for overconvergent F-isocrystals, II: A valuation-theoretic approach

We introduce a valuation-theoretic approach to the problem of semistable reduction (i.e., existence of logarithmic extensions on suitable covers) of overconvergent isocrystals with Frobenius structure. The key tool is the quasicompactness of the Riemann-Zariski space associated to the function field of a variety.Comment: 20 pages; v3: refereed version; corrections to 4.2.1, 4.3.1; some results extended to the partially overconvergent case (replacing Remark 4.3.7