Arithmetic volumes of unitary Shimura varieties
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866915067246673920 |
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| author | Bruinier, Jan Hendrik Howard, Benjamin |
| author_facet | Bruinier, Jan Hendrik Howard, Benjamin |
| contents | The integral model of a $\mathrm{GU}(n-1,1)$ Shimura variety carries a universal abelian scheme over it, and the dual top exterior power of its Lie algebra carries a natural hermitian metric. We express the arithmetic volume of this metrized line bundle, defined as an iterated self-intersection in the arithmetic Chow ring, in terms of logarithmic derivatives of Dirichlet $L$-functions. We also determine the arithmetic volumes of Kudla-Rapoport divisors and relate them to coefficients of Eisenstein series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_11274 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Arithmetic volumes of unitary Shimura varieties Bruinier, Jan Hendrik Howard, Benjamin Number Theory Algebraic Geometry 11G18, 111G50, 14G35, 14G40 The integral model of a $\mathrm{GU}(n-1,1)$ Shimura variety carries a universal abelian scheme over it, and the dual top exterior power of its Lie algebra carries a natural hermitian metric. We express the arithmetic volume of this metrized line bundle, defined as an iterated self-intersection in the arithmetic Chow ring, in terms of logarithmic derivatives of Dirichlet $L$-functions. We also determine the arithmetic volumes of Kudla-Rapoport divisors and relate them to coefficients of Eisenstein series. |
| title | Arithmetic volumes of unitary Shimura varieties |
| topic | Number Theory Algebraic Geometry 11G18, 111G50, 14G35, 14G40 |
| url | https://arxiv.org/abs/2105.11274 |