Endoscopy on SL2-eigenvarieties
In this paper, we study 𝑝-adic endoscopy on eigenvarieties for SL 2 \mathrm{SL}_{2} over totally real fields, taking a geometric perspective. We show that non-automorphic members of endoscopic 𝐿-packets of regular weight contribute eigenvectors to overconvergent cohomology at critically refined endo...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
28. Mai 2024
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| In: |
Journal für die reine und angewandte Mathematik
Year: 2024, Issue: 813, Pages: 1-79 |
| ISSN: | 1435-5345 |
| DOI: | 10.1515/crelle-2024-0026 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1515/crelle-2024-0026 Verlag, lizenzpflichtig, Volltext: https://www.degruyterbrill.com/document/doi/10.1515/crelle-2024-0026/html?lang=de 
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| Author Notes: | by Christian Johansson at Gothenburg and Judith Ludwig at Heidelberg |
| Summary: | In this paper, we study 𝑝-adic endoscopy on eigenvarieties for SL 2 \mathrm{SL}_{2} over totally real fields, taking a geometric perspective. We show that non-automorphic members of endoscopic 𝐿-packets of regular weight contribute eigenvectors to overconvergent cohomology at critically refined endoscopic points on the eigenvariety, and we precisely quantify this contribution. This gives a new perspective on and generalizes previous work of the second author. Our methods are geometric, and are based on showing that the SL 2 \mathrm{SL}_{2} -eigenvariety is locally a quotient of an eigenvariety for GL 2 \mathrm{GL}_{2} , which allows us to explicitly describe the local geometry of the SL 2 \mathrm{SL}_{2} -eigenvariety. In particular, we show that it often fails to be Gorenstein. |
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| Item Description: | Gesehen am 03.09.2024 |
| Physical Description: | Online Resource |
| ISSN: | 1435-5345 |
| DOI: | 10.1515/crelle-2024-0026 |