Geometric Height on Flag Varieties in Positive Characteristic
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912949461843968 |
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| author | Chen, Yue Yuan, Haoyang |
| author_facet | Chen, Yue Yuan, Haoyang |
| contents | Let $k$ be an algebraically closed field of characteristic $p\neq 0$. Let $G$ be a connected reductive group over $k$, $P \subseteq G$ be a parabolic subgroup and $λ: P \longrightarrow \mathbb G_m$ be a strictly anti-dominant character. Let $C$ be a projective smooth curve over $k$ with function field $K=k(C)$ and $F$ be a principal $G$-bundle on $C$. Then $F/P \longrightarrow C$ is a flag bundle and $\mathcal{L}_λ=F \times_P k_λ$ on $F/P$ is a relatively ample line bundle. We compute the height filtration and successive minima of the height function $h_{\mathcal{L}_λ}: X(\overline{K}) \longrightarrow \mathbb{R}$ over the flag variety $X=(F/P)_K$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_10393 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric Height on Flag Varieties in Positive Characteristic Chen, Yue Yuan, Haoyang Number Theory Algebraic Geometry Representation Theory 11G50 Let $k$ be an algebraically closed field of characteristic $p\neq 0$. Let $G$ be a connected reductive group over $k$, $P \subseteq G$ be a parabolic subgroup and $λ: P \longrightarrow \mathbb G_m$ be a strictly anti-dominant character. Let $C$ be a projective smooth curve over $k$ with function field $K=k(C)$ and $F$ be a principal $G$-bundle on $C$. Then $F/P \longrightarrow C$ is a flag bundle and $\mathcal{L}_λ=F \times_P k_λ$ on $F/P$ is a relatively ample line bundle. We compute the height filtration and successive minima of the height function $h_{\mathcal{L}_λ}: X(\overline{K}) \longrightarrow \mathbb{R}$ over the flag variety $X=(F/P)_K$. |
| title | Geometric Height on Flag Varieties in Positive Characteristic |
| topic | Number Theory Algebraic Geometry Representation Theory 11G50 |
| url | https://arxiv.org/abs/2412.10393 |