Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866918124007194624 |
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| author | Takaya, Yuta |
| author_facet | Takaya, Yuta |
| contents | We prove the equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic. This verifies a conjecture made by Rapoport and implies that the results of Nie and Zhou-Zhu can be extended to the whole irreducible components of affine Deligne-Lusztig varieties. The method is to translate the work of Hartl-Viehmann into mixed characteristic and construct local foliations for affine Deligne-Lusztig varieties. This leads us to develop a theory of formal algebraic geometry for perfect schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_13499 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic Takaya, Yuta Algebraic Geometry Number Theory We prove the equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic. This verifies a conjecture made by Rapoport and implies that the results of Nie and Zhou-Zhu can be extended to the whole irreducible components of affine Deligne-Lusztig varieties. The method is to translate the work of Hartl-Viehmann into mixed characteristic and construct local foliations for affine Deligne-Lusztig varieties. This leads us to develop a theory of formal algebraic geometry for perfect schemes. |
| title | Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2212.13499 |