Geometrically irreducible p-adic local systems are de Rham up to a twist

We prove that any geometrically irreducible Q‾p-local system on a smooth algebraic variety over p-adic field K becomes de Rham after twist by character of the Galois group K. In particular, for number associated projective representation fundamental automatically satisfies assumptions relative Fontaine–Mazur conjecture. The proof uses Simpson and Riemann–Hilbert correspondences Diao, Lan, Liu, Zhu Sen operator decompletions those developed Shimizu. Along way, we observe local connected is Hodge–Tate if its stalk at one closed point representation. Moreover, version main theorem systems with arbitrary geometric monodromy, which allows us to conclude action proalgebraic completion π1ét Rham.