论文标题
本地类型的$（γ，g）$ - 捆绑和帕哈里奇集团计划
Local types of $(Γ,G)$-bundles and parahoric group schemes
论文作者
论文摘要
让$ g $成为一个简单的代数集团，这是一个代数封闭的字段$ k $。令$γ$为$ g $的有限群体。我们根据稳定的第一个非阿布莱人组共同体在稳定的$γ$ culve上对本地类型进行分类和计算$（γ，g）$ - 捆绑，稳定稳定器组的第一个非阿布莱群体共同体在腐烂的点上，其系数为$ g $。当$ \ text {char}（k）= 0 $时，我们证明了任何一般简单连接的帕拉卡 - tit-tits group方案都可以来自$（γ，g _ {\ g _ {\ text {ad}}）$ - bundle。我们还证明了该定理的本地版本，即对正式光盘的帕哈里奇集体方案，这是由持续损坏的覆盖物引起的。
Let $G$ be a simple algebraic group over an algebraically closed field $k$. Let $Γ$ be a finite group acting on $G$. We classify and compute the local types of $(Γ, G)$-bundles on a smooth projective $Γ$-curve in terms of the first non-abelian group cohomology of the stabilizer groups at the tamely ramified points with coefficients in $G$. When $\text{char}(k)=0$, we prove that any generically simply-connected parahoric Bruhat--Tits group scheme can arise from a $(Γ,G_{\text{ad}})$-bundle. We also prove a local version of this theorem, i.e. parahoric group schemes over the formal disc arise from constant group schemes via tamely ramified coverings.
