A note on the $p$-adic Galois representations attached to Hilbert modular forms

Abstract

We show that the $p$-adic Galois representations attached to Hilbert modular forms of motivic weight are potentially semistable at all places above $p$ and are compatible with the local Langlands correspondence at these places, proving this for those forms not covered by the previous works of T. Saito and of D. Blasius and J. Rogawski.