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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2507.16827 |
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| _version_ | 1866908664391008256 |
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| author | Bhatta, Bijay Raj |
| author_facet | Bhatta, Bijay Raj |
| contents | We prove the Zilber-Pink conjecture to the intersection of an irreducible Hodge generic algebraic subvariety $ V \subset \mathcal{A}_g$ with special subvarieties of all simple PEL types other than $\mathbb{Z}$, under the assumption of the Large Galois Orbits conjecture. In particular, we establish parameter height bounds for the arithmetic ingredients of the Pila-Zannier strategy in the case of Albert types III and IV. This paper is a sequel to Daw and Orr's paper "Lattices with skew-Hermitian forms over division algebras and unlikely intersections" 2023. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16827 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parameter Height bounds for the Zilber Pink conjecture for PEL types III and IV Bhatta, Bijay Raj Number Theory We prove the Zilber-Pink conjecture to the intersection of an irreducible Hodge generic algebraic subvariety $ V \subset \mathcal{A}_g$ with special subvarieties of all simple PEL types other than $\mathbb{Z}$, under the assumption of the Large Galois Orbits conjecture. In particular, we establish parameter height bounds for the arithmetic ingredients of the Pila-Zannier strategy in the case of Albert types III and IV. This paper is a sequel to Daw and Orr's paper "Lattices with skew-Hermitian forms over division algebras and unlikely intersections" 2023. |
| title | Parameter Height bounds for the Zilber Pink conjecture for PEL types III and IV |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.16827 |