Moduli of $G$-bundles on rigid gerbes over affine curves
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917287847526400 |
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| author | Dillery, Peter |
| author_facet | Dillery, Peter |
| contents | We geometrize the basic cohomology set $H^{1}(\text{Kal}_{F}, G)_{\text{basic}}$ for a global function field $F$. We do this by constructing a v-stack $\text{Bun}_{G,F}^{e}$ which has localization maps to Fargues' analogous stack $\text{Bun}_{G,F_{v}}^{e}$ for all places $v$ of $F$ and whose semistable locus is the disjoint union of $\text{Bun}_{G_{b},F}$ for all $b \in H^{1}(\text{Kott}_{F} \times_{F} \text{Kal}_{F},G)_{\text{basic}}$. We also prove a version of Tate-Nakayama duality for $H^{1}(\text{Kott}_{F} \times_{F} \text{Kal}_{F},G)_{\text{basic}}$, which lets us state a conjectural multiplicity formula for discrete automorphic representations of $G(\mathbb{A}_{F})$ adapted to this new cohomology set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19382 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Moduli of $G$-bundles on rigid gerbes over affine curves Dillery, Peter Number Theory Algebraic Geometry Representation Theory 11E72, 11F70, 11S37 We geometrize the basic cohomology set $H^{1}(\text{Kal}_{F}, G)_{\text{basic}}$ for a global function field $F$. We do this by constructing a v-stack $\text{Bun}_{G,F}^{e}$ which has localization maps to Fargues' analogous stack $\text{Bun}_{G,F_{v}}^{e}$ for all places $v$ of $F$ and whose semistable locus is the disjoint union of $\text{Bun}_{G_{b},F}$ for all $b \in H^{1}(\text{Kott}_{F} \times_{F} \text{Kal}_{F},G)_{\text{basic}}$. We also prove a version of Tate-Nakayama duality for $H^{1}(\text{Kott}_{F} \times_{F} \text{Kal}_{F},G)_{\text{basic}}$, which lets us state a conjectural multiplicity formula for discrete automorphic representations of $G(\mathbb{A}_{F})$ adapted to this new cohomology set. |
| title | Moduli of $G$-bundles on rigid gerbes over affine curves |
| topic | Number Theory Algebraic Geometry Representation Theory 11E72, 11F70, 11S37 |
| url | https://arxiv.org/abs/2602.19382 |