Depth 0 local Langlands via global chtoucas

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

Let G be a split reductive group, F a local function field of characteristic p and a smooth proper curve X together with a place x \in X such that the local field at x is identified with F. In this setting Lafforgue and Genestier have constructed a semisimple Langlands correspondence using the cohomology of stacks of chtoucas on X. In
another direction, DeBacker and Reeder have constructed a depth 0 local Langlands correspondence. In this talk, I will discuss a compatibility statement between the two constructions and their relations to global chtoucas.