标题： $\mathcal{G}$-丛在非连通群概形下的模以及本质上有限丛的非稠密性 显示英文标题

标题： Moduli of $\mathcal{G}$-bundles under nonconnected group schemes and nondensity of essentially finite bundles

摘要： 我们证明在非连通的半单纯群概形 $\mathcal{G}$作用下，主 $\mathcal{G}$-丛在光滑投影曲线 $C$上存在一个射影良好模空间。 我们还证明了模堆栈$\mathcal{G}$-丛分解为有限多个子堆栈$\text{Bun}_{\mathcal{P}}$，每个子堆栈都存在一个在有限群下的torsor$\text{Bun}_{\mathcal{G}_\mathcal{P}}\to \text{Bun}_{\mathcal{P}}$，对于某些连通的半单群概形$\mathcal{G}_\mathcal{P}$在$C$上。 We use this for the second purpose of the article: for any constant connected reductive group $G$, the subset of essentially finite $G$-bundles in the moduli of degree 0 semistable $G$-bundles over $C$ is not dense, unless $G$ is a torus or the genus of $C$ is smaller than 2. We do this by giving an upper bound on the dimension of the closure of the subset of essentially finite $G$-bundles. 显示英文摘要

摘要： We prove the existence of a projective good moduli space of principal $\mathcal{G}$-bundles under nonconnected reductive group schemes $\mathcal{G}$ over a smooth projective curve $C$. We also prove that the moduli stack of $\mathcal{G}$-bundles decomposes into finitely many substacks $\text{Bun}_{\mathcal{P}}$ each admitting a torsor $\text{Bun}_{\mathcal{G}_\mathcal{P}}\to \text{Bun}_{\mathcal{P}}$ under a finite group, for some connected reductive group schemes $\mathcal{G}_\mathcal{P}$ over $C$. We use this for the second purpose of the article: for any constant connected reductive group $G$, the subset of essentially finite $G$-bundles in the moduli of degree 0 semistable $G$-bundles over $C$ is not dense, unless $G$ is a torus or the genus of $C$ is smaller than 2. We do this by giving an upper bound on the dimension of the closure of the subset of essentially finite $G$-bundles.