$L^2$-property for algebraic stacks over local non-archimedean fields
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915752318074880 |
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| author | Kazhdan, David Polishchuk, Alexander |
| author_facet | Kazhdan, David Polishchuk, Alexander |
| contents | We introduce an $L^2$-norm on the space of Schwartz half-densities over algebraic stacks over local non-archimedean fields. We show that these $L^2$-norms are finite for the stacks of $PGL_2$-bundles on $\mathbb{P}^1$ with parabolic structures at $\ge 3$ points. The latter property was conjectured in the context of the analytic Langlands correspondence of arXiv:2103.01509. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14557 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $L^2$-property for algebraic stacks over local non-archimedean fields Kazhdan, David Polishchuk, Alexander Algebraic Geometry Number Theory We introduce an $L^2$-norm on the space of Schwartz half-densities over algebraic stacks over local non-archimedean fields. We show that these $L^2$-norms are finite for the stacks of $PGL_2$-bundles on $\mathbb{P}^1$ with parabolic structures at $\ge 3$ points. The latter property was conjectured in the context of the analytic Langlands correspondence of arXiv:2103.01509. |
| title | $L^2$-property for algebraic stacks over local non-archimedean fields |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2601.14557 |