Léo Poyeton (Université de Bordeaux)

Berger and Colmez have shown how to use the theory of locally analytic vectors of  Schneider and Teitelbaum in order to recover classical Sen theory and to generalize it to arbitrary p-adic Lie extensions. After recalling their constructions, I will explain how some results from Berger can be used to construct rings of periods which “compute” (phi,Gamma)-modules theories and differential de Rham theory. I will then explain what happens when we try to expand the point of view of Berger and Colmez to higher rings of periods and what results one should expect in this case.