Weighted Cohomology, Hodge Theory and Intersection Cohomology of Shimura varieties
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911544494784512 |
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| author | Ni, Mingyu |
| author_facet | Ni, Mingyu |
| contents | We prove that the intersection cohomology of the Baily-Borel compactification of a complex Shimura variety is identified with the top weight quotient of the mixed Hodge structure on the reductive Borel-Serre compactification. This yields canonical cup products and functorial pullbacks on the intersection cohomology. As an application, we introduce canonical cycle classes associated to special cycles, relating analytic geometric volumes of non-compact Shimura varieties to topological terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24464 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weighted Cohomology, Hodge Theory and Intersection Cohomology of Shimura varieties Ni, Mingyu Algebraic Geometry Number Theory 14F43, 14C40, 14G35, 11G18, 11F75 We prove that the intersection cohomology of the Baily-Borel compactification of a complex Shimura variety is identified with the top weight quotient of the mixed Hodge structure on the reductive Borel-Serre compactification. This yields canonical cup products and functorial pullbacks on the intersection cohomology. As an application, we introduce canonical cycle classes associated to special cycles, relating analytic geometric volumes of non-compact Shimura varieties to topological terms. |
| title | Weighted Cohomology, Hodge Theory and Intersection Cohomology of Shimura varieties |
| topic | Algebraic Geometry Number Theory 14F43, 14C40, 14G35, 11G18, 11F75 |
| url | https://arxiv.org/abs/2603.24464 |