On G-isoshtukas over function fields

Abstract

In this paper we classify isogeny classes of global G-shtukas over a smooth projective curve C/F-q (or equivalently s-conjugacy classes in G(F circle times F-q (F) over barq) where F is the field of rational functions of C) by two invariants (kappa) over bar, (nu) over bar extending previous works of Kottwitz. This result can be applied to study points of moduli spaces of G-shtukas and thus is helpful to calculate their cohomology.