Final Report Summary - G-SHTUKAS (Moduli spaces of local G-shtukas)
- We extended the foundations of the theory, i.e. the construction of towers on the generic fiber of the moduli spaces, their cohomology groups and relations to moduli spaces of global G-shtukas.
- We studied the cohomology of the moduli spaces, both of the towers in the generic fiber and of the reduced schemes in the special fiber, so-called affine Deligne-Lusztig varieties. These questions are motivated by the goal to realize local Langlands correspondences.
- Our geometric results on the one hand give insight into fundamental properties of the special fibers of the moduli spaces such as non-emptiness, dimension, and the sets of connected components and of irreducible components. On the other hand we relate moduli spaces of local G-shtukas to corresponding moduli spaces of global G-shtukas via the Newton stratification. These results also led to a parallel theory for the geometry of Shimura varieties and moduli spaces of p-divisible groups.