Zero-dimensional affine Deligne--Lusztig varieties
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929254697009152 |
|---|---|
| author | He, Xuhua Nie, Sian Yu, Qingchao |
| author_facet | He, Xuhua Nie, Sian Yu, Qingchao |
| contents | In this paper, we study the affine Deligne--Lusztig variety $X(μ,b)_K$ and classify all quadruples $(\mathbf{G}, μ, b, K)$ with $\dim X(μ, b)_K=0$. This question was first asked by Rapoport in 2005, who also made an explicit conjecture in the hyperspecial level. We prove that $\dim X(μ,b)_K=0$ if and only if, up to certain Hodge-Newton decomposition condition, the pair $(\mathbf{G}, \{μ\})$ is of extended Lubin-Tate type. We also give a combinatorial description of this condition by the essential gap function on $B(\mathbf{G})$ and the $μ$-ordinary condition for the generic Newton stratum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15310 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zero-dimensional affine Deligne--Lusztig varieties He, Xuhua Nie, Sian Yu, Qingchao Algebraic Geometry Number Theory Representation Theory 20G25, 14G35, 11G25 In this paper, we study the affine Deligne--Lusztig variety $X(μ,b)_K$ and classify all quadruples $(\mathbf{G}, μ, b, K)$ with $\dim X(μ, b)_K=0$. This question was first asked by Rapoport in 2005, who also made an explicit conjecture in the hyperspecial level. We prove that $\dim X(μ,b)_K=0$ if and only if, up to certain Hodge-Newton decomposition condition, the pair $(\mathbf{G}, \{μ\})$ is of extended Lubin-Tate type. We also give a combinatorial description of this condition by the essential gap function on $B(\mathbf{G})$ and the $μ$-ordinary condition for the generic Newton stratum. |
| title | Zero-dimensional affine Deligne--Lusztig varieties |
| topic | Algebraic Geometry Number Theory Representation Theory 20G25, 14G35, 11G25 |
| url | https://arxiv.org/abs/2402.15310 |