Semi-stable and splitting models for unitary Shimura varieties over ramified places. I.
We consider Shimura varieties associated to a unitary group of signature $(n-s,s)$ where n is even. For these varieties, we construct smooth p-adic integral models for $s=1$ and regular p-adic integral models for $s=2$ and $s=3$ over odd primes p which ramify in the imagi...
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| Format: | Article |
| Language: | English |
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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/S2050509425100790/type/journal_article |
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| author | Ioannis Zachos Zhihao Zhao |
| author_facet | Ioannis Zachos Zhihao Zhao |
| author_sort | Ioannis Zachos |
| collection | DOAJ |
| description | We consider Shimura varieties associated to a unitary group of signature
$(n-s,s)$
where n is even. For these varieties, we construct smooth p-adic integral models for
$s=1$
and regular p-adic integral models for
$s=2$
and
$s=3$
over odd primes p which ramify in the imaginary quadratic field with level subgroup at p given by the stabilizer of a
$\pi $
-modular lattice in the hermitian space. Our construction, which has an explicit moduli-theoretic description, is given by an explicit resolution of a corresponding local model. |
| format | Article |
| id | doaj-art-cc3b8e6ba8e6497b85e70d4470a43d40 |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-cc3b8e6ba8e6497b85e70d4470a43d402025-08-20T03:50:58ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2025.10079Semi-stable and splitting models for unitary Shimura varieties over ramified places. I.Ioannis Zachos0Zhihao Zhao1Department of Mathematics, Universität Münster https://ror.org/00pd74e08 , Münster, 48149, GermanyDepartment of Applied Mathematics, University of Science and Technology Beijing https://ror.org/02egmk993 , Beijing, 100083, China; E-mail:We consider Shimura varieties associated to a unitary group of signature $(n-s,s)$ where n is even. For these varieties, we construct smooth p-adic integral models for $s=1$ and regular p-adic integral models for $s=2$ and $s=3$ over odd primes p which ramify in the imaginary quadratic field with level subgroup at p given by the stabilizer of a $\pi $ -modular lattice in the hermitian space. Our construction, which has an explicit moduli-theoretic description, is given by an explicit resolution of a corresponding local model.https://www.cambridge.org/core/product/identifier/S2050509425100790/type/journal_article14G3511G18 |
| spellingShingle | Ioannis Zachos Zhihao Zhao Semi-stable and splitting models for unitary Shimura varieties over ramified places. I. Forum of Mathematics, Sigma 14G35 11G18 |
| title | Semi-stable and splitting models for unitary Shimura varieties over ramified places. I. |
| title_full | Semi-stable and splitting models for unitary Shimura varieties over ramified places. I. |
| title_fullStr | Semi-stable and splitting models for unitary Shimura varieties over ramified places. I. |
| title_full_unstemmed | Semi-stable and splitting models for unitary Shimura varieties over ramified places. I. |
| title_short | Semi-stable and splitting models for unitary Shimura varieties over ramified places. I. |
| title_sort | semi stable and splitting models for unitary shimura varieties over ramified places i |
| topic | 14G35 11G18 |
| url | https://www.cambridge.org/core/product/identifier/S2050509425100790/type/journal_article |
| work_keys_str_mv | AT ioanniszachos semistableandsplittingmodelsforunitaryshimuravarietiesoverramifiedplacesi AT zhihaozhao semistableandsplittingmodelsforunitaryshimuravarietiesoverramifiedplacesi |