Uniformizing the Moduli Stacks of Global G-Shtukas

Arasteh Rad Esmail, Hartl Urs

Abstract

This is the second in a sequence of two articles, in which we propose to view the moduli stacks of global G-shtukas as function field analogs for Shimura varieties. Here G is a parahoric Bruhat-Tits group scheme over a smooth projective curve, and global G-shtukas are generalizations of Drinfeld shtukas and analogs of abelian varieties with additional structure. We prove that the moduli stacks of global G-shtukas are algebraic Deligne-Mumford stacks. They generalize various moduli spaces used by different authors to prove instances of the Langlands program over function fields. In the first article we explained the relation between global G-shtukas and local P-shtukas, which are the function field analogs of p-divisible groups, and we proved the existence of Rapoport-Zink spaces for local P-shtukas. In the present article we use these spaces to (partly) uniformize the moduli stacks of global G-shtukas.