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.

Extremal Cases of Rapoport–zink Spaces

“…Something analogous holds in the function-field case for formal moduli spaces of shtukas (cf. [37]; in this case, the minuscule hypothesis can be dropped). Both classes of formal schemes are very mysterious.…”

Affine Deligne–Lusztig varieties and quantum Bruhat graph

“…Since the underlying topological space of Fl G J is Jacobson, any locally closed subscheme is uniquely determined by its κ-valued points, hence we freely identify X G (µ, b) J with the above set of its geometric points. These varieties play an important role in the study of the special fiber of both Shimura varieties and moduli spaces of shtukas, see [RV14], [Vie18].…”

Extremal cases of Rapoport-Zink spaces

“…Something analogous holds in the function field case for formal moduli spaces of Shtukas, cf. [Vi18] (in the latter case, the minuscule hypothesis can be dropped). Both classes of formal schemes are very mysterious.…”