Seminar

In its original form, p-adic Hodge theory was described in terms of rings of power series which are equipped with certain "Frobenius" endomorphisms, which are injective but not surjective. In the theory of perfectoid algebras and spaces, these rings are typically replaced by rings on which the corresponding Frobenius endomorphisms are bijective, in order to take advantage of better functoriality properties. However, certain constructions do still depend on the "imperfect" base rings; for instance, these give rise to locally analytic representations of a certain p-adic Lie groups, which play a role in the construction of the p-adic Langlands correspondence for GL_2(Q_p). We describe a framework for potentially generalizing this construction by establishing a suitable analogue of the Cherbonnier-Colmez theorem. One case where this plan succeeds is the Lubin-Tate tower, which may have consequences for GL_n(Q_p). (Joint work with Ruochuan Liu.)