Monodromy and Irreducibility of Igusa Varieties
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2021
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910948211556352 |
|---|---|
| author | van Hoften, Pol Xiao, Luciena Xiao |
| author_facet | van Hoften, Pol Xiao, Luciena Xiao |
| contents | We determine the irreducible components of Igusa varieties for Shimura varieties of Hodge type under a mild condition and use that to compute the irreducible components of central leaves. In particular, we show that a strong version of the discrete Hecke orbit conjecture is false in general. Our method combines recent work of D'Addezio on monodromy groups of compatible local systems with a generalisation of a method of Hida, using the Honda--Tate theory for Shimura varieties of Hodge type developed by Kisin--Madapusi--Shin. We also determine the irreducible components of Newton strata in Shimura varieties of Hodge type by combining our methods with recent work of Zhou--Zhu. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_09870 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Monodromy and Irreducibility of Igusa Varieties van Hoften, Pol Xiao, Luciena Xiao Number Theory Algebraic Geometry 11G18, 14G35 We determine the irreducible components of Igusa varieties for Shimura varieties of Hodge type under a mild condition and use that to compute the irreducible components of central leaves. In particular, we show that a strong version of the discrete Hecke orbit conjecture is false in general. Our method combines recent work of D'Addezio on monodromy groups of compatible local systems with a generalisation of a method of Hida, using the Honda--Tate theory for Shimura varieties of Hodge type developed by Kisin--Madapusi--Shin. We also determine the irreducible components of Newton strata in Shimura varieties of Hodge type by combining our methods with recent work of Zhou--Zhu. |
| title | Monodromy and Irreducibility of Igusa Varieties |
| topic | Number Theory Algebraic Geometry 11G18, 14G35 |
| url | https://arxiv.org/abs/2102.09870 |