Mixed Hodge structures and Siegel operators
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916351671533568 |
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| author | Ma, Shouhei |
| author_facet | Ma, Shouhei |
| contents | In this paper we study mixed Hodge structures on the cohomology of locally symmetric varieties and give an application to modular forms. After proving vanishing of some Hodge numbers, we focus on the weight filtration on the last Hodge subspace of the middle degree cohomology. We prove that the weight filtration coincides with the corank filtration on the space of modular forms of canonical weight defined by the Siegel operators, and calculate the graded quotients. As an application, we deduce surjectivity of the total Siegel operators in many cases, and identify an obstruction space in the remaining case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_10979 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mixed Hodge structures and Siegel operators Ma, Shouhei Algebraic Geometry Number Theory 11F75, 14C30, 11F46, 11F55 In this paper we study mixed Hodge structures on the cohomology of locally symmetric varieties and give an application to modular forms. After proving vanishing of some Hodge numbers, we focus on the weight filtration on the last Hodge subspace of the middle degree cohomology. We prove that the weight filtration coincides with the corank filtration on the space of modular forms of canonical weight defined by the Siegel operators, and calculate the graded quotients. As an application, we deduce surjectivity of the total Siegel operators in many cases, and identify an obstruction space in the remaining case. |
| title | Mixed Hodge structures and Siegel operators |
| topic | Algebraic Geometry Number Theory 11F75, 14C30, 11F46, 11F55 |
| url | https://arxiv.org/abs/2305.10979 |