Geodesic
The category $\mathcal{MF}$ in the semistable case
Izvestiya. Mathematics , Tome 80 (2016) no. 5, pp. 849-868.

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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.
Keywords: Fontaine theory, Galois representations. 
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G. Faltings. The category $\mathcal{MF}$ in the semistable case. Izvestiya. Mathematics , Tome 80 (2016) no. 5, pp. 849-868. http://geodesic.mathdoc.fr/item/IM2_2016_80_5_a2/

[3] C. Breuil, “Représentations semi-stables et modules fortement divisibles”, Invent. Math., 136:1 (1999), 89–122 | DOI | MR | Zbl

[4] P. Deligne, M. Rapoport, “Les schémas de modules de courbes elliptiques”, Modular functions of one variable (Univ. Antwerp, Antwerp, 1972), v. II, Lecture Notes in Math., 349, Springer, Berlin, 1973, 143–316 | DOI | MR | Zbl

[5] G. Faltings, Ching-Li Chai, Degeneration of abelian varieties, Ergeb. Math. Grenzgeb. (3), 22, Springer-Verlag, Berlin, 1990, xii+316 pp. | DOI | MR | Zbl

[6] G. Faltings, “Crystalline cohomology and $p$-adic Galois-representations”, Algebraic analysis, geometry, and number theory (Baltimore, MD, 1988), Johns Hopkins Univ. Press, Baltimore, MD, 1989, 25–80 | MR | Zbl

[7] G. Faltings, “Integral crystalline cohomology over very ramified valuation rings”, J. Amer. Math. Soc., 12:1 (1999), 117–144 | DOI | MR | Zbl

[8] J. M. Fontaine, G. Lafaille, “Construction de répresentations $p$-adiques”, Ann. Sci. École Norm. Sup. (4), 15:4 (1982), 547–608 | MR | Zbl

[9] M. Kisin, “Integral models for Shimura varieties of abelian type”, J. Amer. Math. Soc., 23:4 (2010), 967–1012 | DOI | MR | Zbl

[10] A. Vasiu, Integral canonical models for Shimura varieties of Hodge type, Ph. D. Thesis, Princeton Univ., 1994, 70 pp. | MR

[11] A. Vasiu, “Integral canonical models of Shimura varieties of preabelian type”, Asian J. Math., 3:2 (1999), 401–518 | DOI | MR | Zbl