Citation
Fu, Ruide (2025) Two Categorifications of the Local Langlands Correspondence for the Torus. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3fcs-9c06. https://resolver.caltech.edu/CaltechTHESIS:06022025-080334841
Abstract
The stack of local Langlands parameters is a Picard stack when the relevant reductive group is a torus. 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. This second categorification relates to the previous correspondence in the sense that taking the categorical trace construction allows one to reproduce the previous result.
| Item Type: | Thesis (Dissertation (Ph.D.)) | ||||
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| Subject Keywords: | Mathematics, Representation Theory, Number Theory | ||||
| Degree Grantor: | California Institute of Technology | ||||
| Division: | Physics, Mathematics and Astronomy | ||||
| Major Option: | Mathematics | ||||
| Thesis Availability: | Not set | ||||
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| Defense Date: | 14 May 2025 | ||||
| Record Number: | CaltechTHESIS:06022025-080334841 | ||||
| Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:06022025-080334841 | ||||
| DOI: | 10.7907/3fcs-9c06 | ||||
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| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||
| ID Code: | 17359 | ||||
| Collection: | CaltechTHESIS | ||||
| Deposited By: | Frid Fu | ||||
| Deposited On: | 05 Jun 2025 21:08 | ||||
| Last Modified: | 05 Jun 2025 21:08 |
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