Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu)
We construct explicit generating series of arithmetic extensions of Kudla’s special divisors on integral models of unitary Shimura varieties over CM fields with arbitrary split levels and prove that they are modular forms valued in the arithmetic Chow groups. This provides a partial solution to Kudl...
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425000003/type/journal_article |
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| author | Congling Qiu Yujie Xu |
| author_facet | Congling Qiu Yujie Xu |
| author_sort | Congling Qiu |
| collection | DOAJ |
| description | We construct explicit generating series of arithmetic extensions of Kudla’s special divisors on integral models of unitary Shimura varieties over CM fields with arbitrary split levels and prove that they are modular forms valued in the arithmetic Chow groups. This provides a partial solution to Kudla’s modularity problem. The main ingredient in our construction is S. Zhang’s theory of admissible arithmetic divisors. The main ingredient in the proof is an arithmetic mixed Siegel-Weil formula. |
| format | Article |
| id | doaj-art-55a9020e8c7c435e8933ccbbc40f7b6a |
| institution | DOAJ |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-55a9020e8c7c435e8933ccbbc40f7b6a2025-08-20T03:16:39ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/S2050509425000003Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu)Congling Qiu0https://orcid.org/0000-0002-1056-530XYujie Xu1https://orcid.org/0000-0003-3023-3609Department of Mathematics, https://ror.org/03v76x132Yale University, New Haven, CT 06520, U.S.A.Department of Mathematics, Columbia University, New York, NY 10027, U.S.A.; E-mail:We construct explicit generating series of arithmetic extensions of Kudla’s special divisors on integral models of unitary Shimura varieties over CM fields with arbitrary split levels and prove that they are modular forms valued in the arithmetic Chow groups. This provides a partial solution to Kudla’s modularity problem. The main ingredient in our construction is S. Zhang’s theory of admissible arithmetic divisors. The main ingredient in the proof is an arithmetic mixed Siegel-Weil formula.https://www.cambridge.org/core/product/identifier/S2050509425000003/type/journal_article11G1811F2714G40 |
| spellingShingle | Congling Qiu Yujie Xu Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu) Forum of Mathematics, Sigma 11G18 11F27 14G40 |
| title | Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu) |
| title_full | Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu) |
| title_fullStr | Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu) |
| title_full_unstemmed | Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu) |
| title_short | Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu) |
| title_sort | modularity of arithmetic special divisors for unitary shimura varieties with an appendix by yujie xu |
| topic | 11G18 11F27 14G40 |
| url | https://www.cambridge.org/core/product/identifier/S2050509425000003/type/journal_article |
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