Published February 2025
| Version Published
Journal Article
Open
Algebraic Varieties and Automorphic Functions
Creators
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1.
University of Vienna
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2.
California Institute of Technology
Abstract
Let (G, X) be a Shimura datum, let Ω be a connected component of X, let Γ be a congruence subgroup of G(ℚ)⁺, and consider the quotient map q : Ω → S : = Γ\Ω. Consider the Harish-Chandra embedding Ω ⊂ ℂ^N, where N = dim X. We prove two results that give geometric conditions that, if satisfied by an algebraic variety V ⊂ ℂ^N x S, ensure that there is a Zariski dense subset of V of points of the form (x, q(x)).
Copyright and License
© The Author(s) 2025. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (https://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Acknowledgement
We wish to thank the anonymous referees for their valuable comments that helped improve the presentation of this article.
Communicated by Jonathan Pila.
Funding
This work was supported by NSF RTG [DMS-1646385 to S.E. and R.Z.]; and the EPSRC fellowship [EP/T018461/1 to S.E.].
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2107.10392 (arXiv)
Funding
- National Science Foundation
- DMS-1646385
- Engineering and Physical Sciences Research Council
- EP/T018461/1
Dates
- Accepted
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2025-01-28
- Available
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2025-02-18Published