The category $\mathcal{MF}$ in the semistable case

The categories $\mathcal{MF}$ over discrete valuation rings were introduced by J. M. Fontaine as crystalline objects one might hope to associate with Galois representations. The definition was later extended to smooth base-schemes. Here we give a further extension to semistable schemes. As an application we show that certain Shimura varieties have semistable models.