The $\ell$-modular local theta correspondence
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908450710093824 |
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| author | Trias, Justin |
| author_facet | Trias, Justin |
| contents | We study the validity of the local theta correspondence over a non-archimedean local field in the context of modular representation theory \textit{i.e.} for representations with coefficient fields of positive characteristic. For a symplectic-orthogonal or a unitary-unitary dual pair over a $p$-adic field, we obtain a bijective correspondence, as long as the characteristic of the coefficient field is large enough compared to the size of the dual pair, and call it the modular local theta correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11421 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $\ell$-modular local theta correspondence Trias, Justin Representation Theory 11F27, 20C20, 22E50 We study the validity of the local theta correspondence over a non-archimedean local field in the context of modular representation theory \textit{i.e.} for representations with coefficient fields of positive characteristic. For a symplectic-orthogonal or a unitary-unitary dual pair over a $p$-adic field, we obtain a bijective correspondence, as long as the characteristic of the coefficient field is large enough compared to the size of the dual pair, and call it the modular local theta correspondence. |
| title | The $\ell$-modular local theta correspondence |
| topic | Representation Theory 11F27, 20C20, 22E50 |
| url | https://arxiv.org/abs/2507.11421 |