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Construction of semi-stable $$p$$-adic representations. (Construction de représentations $$p$$-adiques semi-stables.) (French) Zbl 0907.14006
Let $$k$$ be a perfect field of characteristic $$p > 0$$ and let $$W$$ denote the ring of Witt vectors of $$k$$ with quotient field $$K_0$$. In Ann. Sci. Éc. Norm. Supér., IV. Sér. 15, 547-608 (1982; Zbl 0579.14037), J.-M. Fontaine and G. Laffaille constructed crystalline representations of the absolute Galois group $$G$$ of $$K_0$$ via strongly divisible $$W$$-modules. The author extends this approach to semi-stable representations of $$G$$ using ideas of G. Faltings [J. Algebr. Geom. 1, No. 1, 61-81 (1992; Zbl 0813.14012)]. In the special case of dimension $$2$$ he constructs all $$2$$-dimensional semi-stable $$p$$-adic representations of $$G$$ with differences in Hodge-Tate weights not exceeding $$p-2$$.

##### MSC:
 14F30 $$p$$-adic cohomology, crystalline cohomology 13K05 Witt vectors and related rings (MSC2000)
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