A remark on potentially semi-stable representations of Hodge-Tate type (0,1)

الأصل · EN

In this note we complement a part of a theorem of Fontaine-Mazur. We show that if (V,ρ) is an irreducible finite dimensional representation of the Galois group Gal(K/K) of a finite extension of Kₚ, of Hodge-Tate type (0,1) then it is potentially semi-stable if and only if it is potentially crystalline. This was proved by Fontaine-Mazur for dimension two and p≥ 5 by their classfication theorem.