Moduli spaces of local G-shtukas

Abstract

We give an overview of the theory of local G-shtukas and their moduli spaces that were introduced in joint work of U.~Hartl and the author, and in the past years studied by many people. We also discuss relations to moduli of global G-shtukas, properties of their special fiber through affine Deligne-Lusztig varieties and of their generic fiber, such as the period map.