At the end of [*Fontaine’s rings and p-adic L-functions*](http://staff.ustc.edu.cn/~yiouyang/colmez.pdf), P. Colmez states a Theorem 8.4.8 ([click here](https://i.stack.imgur.com/JEz0b.png)) of Faltings-Tusji-Saito without references.


So I am wondering is there any references for this theorem?



Reference on a result on local Galois representation associated to classic modular form in p-adic Hodge theory
The three articles referenced presented in logical order of exposition are respectively


Faltings, Gerd *Hodge-Tate structures and modular forms* Math. Ann. 278 (1987)


Tsuji, Takeshi
*$p$-adic étale cohomology and crystalline cohomology in the semi-stable reduction case.* Invent. Math. 137 (1999)


and


Saito, Takeshi
*Modular forms and $p$-adic Hodge theory.* 
Invent. Math. 129 (1997)


