Positivity of automorphic vector bundles on unitary Shimura varieties
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909008632217600 |
|---|---|
| author | Yang, Deding |
| author_facet | Yang, Deding |
| contents | Let $X$ be the special fiber of a unitary Shimura variety of hyperspecial level at a prime $p$ inert in the totally real field $F$. Let $Y\to X$ be the associated flag space. For every $L$-dominant weight $λ$, let $\mathcal{L}_Y(λ)$ denote the corresponding automorphic line bundle. We give an explicit necessary and sufficient criterion, in terms of the signature data and the coordinates of $λ$, for the ampleness of $\mathcal{L}_Y(λ)$. %, which effectively detects the coherent cohomology of automorphic vector bundles on $X$. The criterion generalizes the known ample cone for Hilbert modular and $U(2)$-Shimura varieties. The proof develops the machinery of the description of certain Ekedahl--Oort strata, a geometric Jacquet--Langlands correspondence between strata of unitary Shimura varieties with different signatures, and the construction of stratum Hasse invariants, and introduced a way to systematically deal with combinatorical data in the higher rank case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08119 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positivity of automorphic vector bundles on unitary Shimura varieties Yang, Deding Number Theory Algebraic Geometry Let $X$ be the special fiber of a unitary Shimura variety of hyperspecial level at a prime $p$ inert in the totally real field $F$. Let $Y\to X$ be the associated flag space. For every $L$-dominant weight $λ$, let $\mathcal{L}_Y(λ)$ denote the corresponding automorphic line bundle. We give an explicit necessary and sufficient criterion, in terms of the signature data and the coordinates of $λ$, for the ampleness of $\mathcal{L}_Y(λ)$. %, which effectively detects the coherent cohomology of automorphic vector bundles on $X$. The criterion generalizes the known ample cone for Hilbert modular and $U(2)$-Shimura varieties. The proof develops the machinery of the description of certain Ekedahl--Oort strata, a geometric Jacquet--Langlands correspondence between strata of unitary Shimura varieties with different signatures, and the construction of stratum Hasse invariants, and introduced a way to systematically deal with combinatorical data in the higher rank case. |
| title | Positivity of automorphic vector bundles on unitary Shimura varieties |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2503.08119 |