Locally analytic vectors and local Shimura varieties

Contact: Peter Scholze (scholze@mpim-bonn.mpg.de)

(Joint work with Gabriel Dospinescu). In this talk we report some progress in the study of the locally analytic vectors of proétale period sheaves appearing in (rational) p-adic Hodge theory. The most important example for us will be local Shimura varieties, in particular those arising from a local Shimura datum (G,b,μ) with b basic. We focus our attention in the Lubin-Tate and Drinfeld tower, obtaining as a consequence that the Jacquet-Langlands functor of Scholze is compatible with the passage to locally analytic vectors.