SFB 878
Einsteinstraße 62
D-48149 Münster
Tel.: +49 251 83-33730
Fax: +49 251 83-32720


Uniformizing The Moduli Stacks of Global G-Shtukas

Urs Hartl, Esmail Arasteh Rad,
published 2014-02-12

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.

Impressum | © 2007 FB10 WWU Münster
Universität Münster
Schlossplatz 2 - 48149 Münster
Tel.: +49 (251) 83-0 - Fax: +49 (251) 83-3 20 90