Teacher: Denis Benois
Program
1) Galois absolute group of local fields. Ramification filtration.
2) Witt vectors.
3) p-adic representations of a field of characteristic p.
Hilbert 90 for GL(n).
3) Fontaine approach: B-admissible representations. Examples
4) Sen Theory. Hodge-Tate representations.
5) Ring of padic periods.
6) Formal groups. Lubin-Tate Theory. p-adic periods of formal groups.
7) Filtered Dieudonné’s modules.
8) Classification of p-adic representations (crystalline, semistable,
de Rham).
9) Wealy admissible representations. Fontaine conjecture.
Case of formal groups of dimension 1.
If time permits:
10) Introduction to the Fontaine-Fargues curve.