A03 Special cycles on moduli spaces of G-shtukas

Moduli stacks of global G-shtukas are the function field analogue of Shimura varieties. Their geometry was investigated by the PI and his collaborators. The long term goal of the project is to investigate arithmetic properties of these moduli stacks, special cycles on them and the intersection numbers of the latter. In particular, we want to develop a function field analogue of the Kudla programme for Shimura varieties and prove arithmetic fundamental lemmas for function fields.