Overconvergent Eichler-Shimura morphisms for $\mathrm{GSp}_4$
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| Format: | Preprint |
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2025
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| _version_ | 1866913872200335360 |
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| author | Diao, Hansheng Rosso, Giovanni Wu, Ju-Feng |
| author_facet | Diao, Hansheng Rosso, Giovanni Wu, Ju-Feng |
| contents | We construct explicit Eichler-Shimura morphisms for families of overconvergent Siegel modular forms of genus two. These can be viewed as $p$-adic interpolations of the Eichler-Shimura decomposition of Faltings-Chai for classical Siegel modular forms. In particular, we are able to $p$-adically interpolate the entire decomposition, extending our previous work on the $H^0$-part. The key new inputs are the higher Coleman theory of Boxer-Pilloni and a theory of pro-Kummer étale cohomology with supports. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Overconvergent Eichler-Shimura morphisms for $\mathrm{GSp}_4$ Diao, Hansheng Rosso, Giovanni Wu, Ju-Feng Number Theory Algebraic Geometry We construct explicit Eichler-Shimura morphisms for families of overconvergent Siegel modular forms of genus two. These can be viewed as $p$-adic interpolations of the Eichler-Shimura decomposition of Faltings-Chai for classical Siegel modular forms. In particular, we are able to $p$-adically interpolate the entire decomposition, extending our previous work on the $H^0$-part. The key new inputs are the higher Coleman theory of Boxer-Pilloni and a theory of pro-Kummer étale cohomology with supports. |
| title | Overconvergent Eichler-Shimura morphisms for $\mathrm{GSp}_4$ |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2506.02643 |