$\mathrm{D}-\mathrm{mod}(\mathrm{Bun}_G^\mathrm{I})$ is Compactly Generated
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912138418716672 |
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| author | Nam, Taeuk |
| author_facet | Nam, Taeuk |
| contents | Drinfeld and Gaitsgory proved that $\mathrm{D}-\mathrm{mod}(\mathrm{Bun}_G)$ is compactly generated. Let $\mathrm{Bun}_G^{\mathrm{I}}$ be the algebraic stack of principal $G$-bundles on $X$ together with Iwahori level structure at a fixed point $x \in X$. More generally, for a finite collection of points $x_1, ..., x_k \in X$, let $\mathrm{Bun}_G^{(\mathrm{I}; x_1, ..., x_k)}$ be the algebraic stack of principal $G$-bundles on $X$ together with Iwahori level structure at each point $x_j$. We will show that $\mathrm{D}-\mathrm{mod}(\mathrm{Bun}_G^{\mathrm{I}})$ and $\mathrm{D}-\mathrm{mod}(\mathrm{Bun}_G^{(\mathrm{I}; x_1, ..., x_k)})$ are compactly generated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03057 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\mathrm{D}-\mathrm{mod}(\mathrm{Bun}_G^\mathrm{I})$ is Compactly Generated Nam, Taeuk Algebraic Geometry Drinfeld and Gaitsgory proved that $\mathrm{D}-\mathrm{mod}(\mathrm{Bun}_G)$ is compactly generated. Let $\mathrm{Bun}_G^{\mathrm{I}}$ be the algebraic stack of principal $G$-bundles on $X$ together with Iwahori level structure at a fixed point $x \in X$. More generally, for a finite collection of points $x_1, ..., x_k \in X$, let $\mathrm{Bun}_G^{(\mathrm{I}; x_1, ..., x_k)}$ be the algebraic stack of principal $G$-bundles on $X$ together with Iwahori level structure at each point $x_j$. We will show that $\mathrm{D}-\mathrm{mod}(\mathrm{Bun}_G^{\mathrm{I}})$ and $\mathrm{D}-\mathrm{mod}(\mathrm{Bun}_G^{(\mathrm{I}; x_1, ..., x_k)})$ are compactly generated. |
| title | $\mathrm{D}-\mathrm{mod}(\mathrm{Bun}_G^\mathrm{I})$ is Compactly Generated |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2411.03057 |