This course covers the structure theory of Galois groups of local fields, the rings of Witt vectors, the classification of p-adic representations via phi-modules, the tilting construction from the theory of perfectoid spaces, the ring of de Rham periods and the notion of a de Rham representation.
Understanding the construction of the ring of de Rham periods.
In addition to the subjects mentioned in the abstract the course included the basic theory of local fields, l-adic local Galois representations, an oveview of perfectoid fields, the statements of the theorems of Fontaine-Winterberger and Faltings-Tsuji.
J.-M. Fontaine, Y. Ouyang. Theory of p-adic Galois representations. O. Brinon, B. Conrad. CMI summer school notes on p-adic Hodge theory.