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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1906.04008 |
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| _version_ | 1866909419575443456 |
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| author | van Hoften, Pol |
| author_facet | van Hoften, Pol |
| contents | We study the Picard-Lefschetz formula for the Siegel modular threefold of paramodular level and prove the weight-monodromy conjecture for its middle degree inner cohomology with arbitrary automorphic coefficients. We give some applications to the Langlands programme: Using Rapoport-Zink uniformisation of the supersingular locus of the special fiber, we construct a geometric Jacquet-Langlands correspondence between $\operatorname{GSp}_4$ and a definite inner form, proving a conjecture of Ibukiyama. We also prove an integral version of the weight-monodromy conjecture and use it to deduce a level lowering result for cohomological cuspidal automorphic representations of $\operatorname{GSp}_4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_04008 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A geometric Jacquet-Langlands correspondence for paramodular Siegel threefolds van Hoften, Pol Number Theory Algebraic Geometry 11G18 We study the Picard-Lefschetz formula for the Siegel modular threefold of paramodular level and prove the weight-monodromy conjecture for its middle degree inner cohomology with arbitrary automorphic coefficients. We give some applications to the Langlands programme: Using Rapoport-Zink uniformisation of the supersingular locus of the special fiber, we construct a geometric Jacquet-Langlands correspondence between $\operatorname{GSp}_4$ and a definite inner form, proving a conjecture of Ibukiyama. We also prove an integral version of the weight-monodromy conjecture and use it to deduce a level lowering result for cohomological cuspidal automorphic representations of $\operatorname{GSp}_4$. |
| title | A geometric Jacquet-Langlands correspondence for paramodular Siegel threefolds |
| topic | Number Theory Algebraic Geometry 11G18 |
| url | https://arxiv.org/abs/1906.04008 |