Logo

Mathematical Sciences Research Institute

Home » NGM Research Seminar: Locally analytic vectors via decompletion: variations on a theme of Cherbonnier-Colmez

Seminar

NGM Research Seminar: Locally analytic vectors via decompletion: variations on a theme of Cherbonnier-Colmez November 13, 2014 (01:30 PM PST - 02:20 PM PST)
Parent Program:
Location: MSRI: Simons Auditorium
Speaker(s) Kiran Kedlaya (University of California, San Diego)
Description No Description
Video
No Video Uploaded
Abstract/Media

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.)

No Notes/Supplements Uploaded No Video Files Uploaded