Two Categorifications of the Local Langlands Correspondence for Tori
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917071482257408 |
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| author | Fu, Ruide |
| author_facet | Fu, Ruide |
| contents | The stack of local Langlands parameters for a torus is a Picard stack. In this article, we explicitly determine its Picard dual and show that the Fourier-Mukai transform gives rise to the integral categorical local Langlands correspondence for the torus. This is the categorification of the local Langlands correspondence and answers a conjecture of X. Zhu. Moreover, we establish a geometric version of this correspondence, whose categorical trace reproduces the previous result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07478 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two Categorifications of the Local Langlands Correspondence for Tori Fu, Ruide Representation Theory The stack of local Langlands parameters for a torus is a Picard stack. In this article, we explicitly determine its Picard dual and show that the Fourier-Mukai transform gives rise to the integral categorical local Langlands correspondence for the torus. This is the categorification of the local Langlands correspondence and answers a conjecture of X. Zhu. Moreover, we establish a geometric version of this correspondence, whose categorical trace reproduces the previous result. |
| title | Two Categorifications of the Local Langlands Correspondence for Tori |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2511.07478 |