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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2106.00094 |
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| _version_ | 1866914459260289024 |
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| author | Diao, Hansheng Rosso, Giovanni Wu, Ju-Feng |
| author_facet | Diao, Hansheng Rosso, Giovanni Wu, Ju-Feng |
| contents | The aim of this paper is twofold. We first present a construction of the overconvergent automorphic sheaves for Siegel modular forms by generalising the perfectoid method, originally introduced by Chojecki--Hansen--Johansson for automorphic forms on compact Shimura curves over $\mathbf{Q}$. The global sections of these automorphic sheaves are precisely the overconvergent Siegel modular forms. In particular, one can compare these automorphic sheaves with the ones constructed by Andreatta--Iovita--Pilloni. Secondly, we establish an (explicit) overconvergent Eichler--Shimura morphism for Siegel modular forms, generalising the result of Andreatta--Iovita--Stevens for the elliptic modular forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_00094 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Perfectoid overconvergent Siegel modular forms and the overconvergent Eichler--Shimura morphism Diao, Hansheng Rosso, Giovanni Wu, Ju-Feng Number Theory The aim of this paper is twofold. We first present a construction of the overconvergent automorphic sheaves for Siegel modular forms by generalising the perfectoid method, originally introduced by Chojecki--Hansen--Johansson for automorphic forms on compact Shimura curves over $\mathbf{Q}$. The global sections of these automorphic sheaves are precisely the overconvergent Siegel modular forms. In particular, one can compare these automorphic sheaves with the ones constructed by Andreatta--Iovita--Pilloni. Secondly, we establish an (explicit) overconvergent Eichler--Shimura morphism for Siegel modular forms, generalising the result of Andreatta--Iovita--Stevens for the elliptic modular forms. |
| title | Perfectoid overconvergent Siegel modular forms and the overconvergent Eichler--Shimura morphism |
| topic | Number Theory |
| url | https://arxiv.org/abs/2106.00094 |