Geometry of the Bianchi eigenvariety around non-cuspidal points and strong multiplicity-one results
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910761291350016 |
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| author | Salazar, Daniel Barrera Palacios, Luis Santiago |
| author_facet | Salazar, Daniel Barrera Palacios, Luis Santiago |
| contents | Let $K$ be an imaginary quadratic field. In this article, we study the local geometry of the Bianchi eigenvariety around non-cuspidal classical points, in particular, ordinary non-cuspidal base change points. To perform this study we introduce Bianchi Eisenstein eigensystems and prove strong multiplicity-one results on the cohomology of the corresponding Bianchi threefolds. We believe these results are of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18045 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometry of the Bianchi eigenvariety around non-cuspidal points and strong multiplicity-one results Salazar, Daniel Barrera Palacios, Luis Santiago Number Theory Let $K$ be an imaginary quadratic field. In this article, we study the local geometry of the Bianchi eigenvariety around non-cuspidal classical points, in particular, ordinary non-cuspidal base change points. To perform this study we introduce Bianchi Eisenstein eigensystems and prove strong multiplicity-one results on the cohomology of the corresponding Bianchi threefolds. We believe these results are of independent interest. |
| title | Geometry of the Bianchi eigenvariety around non-cuspidal points and strong multiplicity-one results |
| topic | Number Theory |
| url | https://arxiv.org/abs/2412.18045 |