From the 1980s to 1990s, J.-M. Fontaine constructed an equivalence of categories between the category of p-adic representations and the category of (φ,Γ)-modules. In this paper, we determine the (φ,Γ)-modules corresponding to crystalline representations. This result can be seen, in a sense, as a generalization of Wach modules in the ramified case.
I made a poster (in Japanese).
I apologize for the mistake in the proof of Theorem 2.27. In that proof, we showed the injectivity of the K_0-linear homomorphism f by using reduction modulo p_crys. However, this argument does not work, since \overline{A_\infty} is not p-adically separated. The mistake can be corrected by using Remark 2.19.