講演者

Stefan Reppen氏 （ストックホルム大学・東京大学）

会場

理学部１号館３階基礎数理演習室

アブストラクト

Let $C$ be a smooth, connected projective curve over an algebraically closed field $k$ of characteristic 0, and let $G$ be a non-connected reductive group over $k$. I will explain how to decompose the stack of $G$-bundles $\text{Bun}_G$ into open and closed substacks $X_i$ which admits finite torsors $\text{Bun}_{\mathcal{G}_i} \to X_i$, for some connected reductive group schemes $\mathcal{G}_i$ over $C$. I explain how to use this to obtain a projective good moduli space of semistable $G$-bundles over $C$, for a suitable notion of semistability. Finally, after stating a result concerning finite subgroups of connected reductive groups over $k$, I explain how to see that essentially finite $H$-bundles are not dense in the moduli space of semistable degree 0 $H$-bundles, for any connected reductive group $H$ not equal to a torus.