Schwartz $κ$-densities for the moduli stack of rank $2$ bundles on a curve over a local field
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910593987903488 |
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| author | Braverman, Alexander Kazhdan, David Polishchuk, Alexander |
| author_facet | Braverman, Alexander Kazhdan, David Polishchuk, Alexander |
| contents | Let $\rm{Bun}$ be the moduli stack of rank $2$ bundles with fixed determinant on a smooth proper curve $C$ over a local field $F$. We show how to associate with a Schwartz $κ$-density, for $\rm{Re}(κ)\ge 1/2$, a smooth function on the corresponding coarse moduli space of very stable bundles. In the non-archimedean case we also prove that the stack $\rm{Bun}$ is $κ$-bounded in the sense of Definition 2.10 of [arXiv:2112.08139] for any $κ\in\mathbb{C}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01037 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Schwartz $κ$-densities for the moduli stack of rank $2$ bundles on a curve over a local field Braverman, Alexander Kazhdan, David Polishchuk, Alexander Algebraic Geometry Number Theory Representation Theory Let $\rm{Bun}$ be the moduli stack of rank $2$ bundles with fixed determinant on a smooth proper curve $C$ over a local field $F$. We show how to associate with a Schwartz $κ$-density, for $\rm{Re}(κ)\ge 1/2$, a smooth function on the corresponding coarse moduli space of very stable bundles. In the non-archimedean case we also prove that the stack $\rm{Bun}$ is $κ$-bounded in the sense of Definition 2.10 of [arXiv:2112.08139] for any $κ\in\mathbb{C}$. |
| title | Schwartz $κ$-densities for the moduli stack of rank $2$ bundles on a curve over a local field |
| topic | Algebraic Geometry Number Theory Representation Theory |
| url | https://arxiv.org/abs/2401.01037 |