The supersingular locus of the Shimura variety of $\mathrm{GU}(2,n-2)$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866912484346036224 |
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| author | Fox, Maria Imai, Naoki |
| author_facet | Fox, Maria Imai, Naoki |
| contents | We study the supersingular locus of a reduction at an inert prime of the Shimura variety attached to $\mathrm{GU}(2,n-2)$. More concretely, we realize irreducible components of the supersingular locus as closed subschemes of flag schemes over Deligne--Lusztig varieties defined by explicit conditions after taking perfections. Moreover we study the intersections of the irreducible components. Stratifications of Deligne--Lusztig varieties defined using powers of Frobenius action appear in the description of the intersections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_03584 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The supersingular locus of the Shimura variety of $\mathrm{GU}(2,n-2)$ Fox, Maria Imai, Naoki Number Theory Algebraic Geometry 11G18, 14M15 We study the supersingular locus of a reduction at an inert prime of the Shimura variety attached to $\mathrm{GU}(2,n-2)$. More concretely, we realize irreducible components of the supersingular locus as closed subschemes of flag schemes over Deligne--Lusztig varieties defined by explicit conditions after taking perfections. Moreover we study the intersections of the irreducible components. Stratifications of Deligne--Lusztig varieties defined using powers of Frobenius action appear in the description of the intersections. |
| title | The supersingular locus of the Shimura variety of $\mathrm{GU}(2,n-2)$ |
| topic | Number Theory Algebraic Geometry 11G18, 14M15 |
| url | https://arxiv.org/abs/2108.03584 |