On the cohomological dimension of Siegel modular varieties and the modularity of formal Siegel modular forms
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917064021639168 |
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| author | Fan, Haocheng |
| author_facet | Fan, Haocheng |
| contents | We prove that the coherent cohomological dimension of the Siegel modular variety $A_{g,Γ}$ is at most $g(g+1)/2-2$ for $g\geq 2$. As a corollary, we show that the boundary of the compactified Siegel modular variety satisfies the Grothendieck-Lefschetz condition. This implies, in particular, that formal Siegel modular forms of genus $g\geq2$ are automatically classical Siegel modular forms. Our result generalizes the work of Bruinier and Raum on the modularity of formal Siegel modular forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00799 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the cohomological dimension of Siegel modular varieties and the modularity of formal Siegel modular forms Fan, Haocheng Number Theory Algebraic Geometry We prove that the coherent cohomological dimension of the Siegel modular variety $A_{g,Γ}$ is at most $g(g+1)/2-2$ for $g\geq 2$. As a corollary, we show that the boundary of the compactified Siegel modular variety satisfies the Grothendieck-Lefschetz condition. This implies, in particular, that formal Siegel modular forms of genus $g\geq2$ are automatically classical Siegel modular forms. Our result generalizes the work of Bruinier and Raum on the modularity of formal Siegel modular forms. |
| title | On the cohomological dimension of Siegel modular varieties and the modularity of formal Siegel modular forms |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2511.00799 |