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

在本文中，我们全球进行分类中原衍类\（\ mathsf {G} \） -shtukas通过平滑曲线投影\（C / {\ mathbb {F}} _ q \） （或等效\（\西格玛\） -conjugacy类在\（\ mathsf {G}（\ mathsf {F} \ otimes _ {{\ mathbb {F}} _ q} \划线{{\ mathbb {F}} _ q}）\）其中\（\ mathsf {F } \)是C )的有理函数域，由两个不变量\({\bar{\kappa }},{\bar{\nu }}\)扩展 Kottwitz 之前的工作。该结果可用于研究\(\mathsf {G} \) -shtukas模空间的点，从而有助于计算它们的上同调。