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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.01129 |
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| _version_ | 1866910469392957440 |
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| author | Hellmann, Eugen Hernandez, Valentin Schraen, Benjamin |
| author_facet | Hellmann, Eugen Hernandez, Valentin Schraen, Benjamin |
| contents | We prove the existence of non-classical $p$-adic automorphic eigenforms associated to a classical system of eigenvalues on definite unitary groups in $3$ variables. These eigenforms are associated to Galois representations which are crystalline but very critical at $p$. We use patching techniques related to the trianguline variety of local Galois representations and its local model. The new input is a comparison of the coherent sheaves appearing in the patching process with coherent sheaves on the Grothendieck--Springer version of the Steinberg variety given by a functor constructed by Bezrukavnikov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01129 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Patching and multiplicities of p-adic eigenforms Hellmann, Eugen Hernandez, Valentin Schraen, Benjamin Number Theory Algebraic Geometry We prove the existence of non-classical $p$-adic automorphic eigenforms associated to a classical system of eigenvalues on definite unitary groups in $3$ variables. These eigenforms are associated to Galois representations which are crystalline but very critical at $p$. We use patching techniques related to the trianguline variety of local Galois representations and its local model. The new input is a comparison of the coherent sheaves appearing in the patching process with coherent sheaves on the Grothendieck--Springer version of the Steinberg variety given by a functor constructed by Bezrukavnikov. |
| title | Patching and multiplicities of p-adic eigenforms |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2406.01129 |