Algebraic Varieties and Automorphic Functions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909470286675968 |
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| author | Eterović, Sebastian Zhao, Roy |
| author_facet | Eterović, Sebastian Zhao, Roy |
| contents | Let $(G, X)$ be a Shimura datum, let $Ω$ be a connected component of $X$, let $Γ$ be a congruence subgroup of $G(\mathbb{Q})^{+}$, and consider the quotient map $q: Ω\to S:=Γ\backslash Ω$. Consider the Harish-Chandra embedding $Ω\subset\mathbb{C}^{N}$, where $N=\dim X$. We prove two results that give geometric conditions which if satisfied by an algebraic variety $V \subset \mathbb{C}^{N} \times S$, ensure that there is a Zariski dense subset of $V$ of points of the form $(x,q(x))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_10392 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Algebraic Varieties and Automorphic Functions Eterović, Sebastian Zhao, Roy Algebraic Geometry Number Theory Let $(G, X)$ be a Shimura datum, let $Ω$ be a connected component of $X$, let $Γ$ be a congruence subgroup of $G(\mathbb{Q})^{+}$, and consider the quotient map $q: Ω\to S:=Γ\backslash Ω$. Consider the Harish-Chandra embedding $Ω\subset\mathbb{C}^{N}$, where $N=\dim X$. We prove two results that give geometric conditions which if satisfied by an algebraic variety $V \subset \mathbb{C}^{N} \times S$, ensure that there is a Zariski dense subset of $V$ of points of the form $(x,q(x))$. |
| title | Algebraic Varieties and Automorphic Functions |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2107.10392 |