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This is a Quantitative Study study.

October 8, 2025Open Access

Parameter Height bounds for the Zilber Pink conjecture for PEL types III and IV

Key Points

Establishing parameter height bounds confirms aspects of the zilber-pink conjecture in algebraic geometry, and suggests further implications for Galois orbits.
The Pila-Zannier strategy is applied to derive results specific to algebraic subvarieties under the assumption of large Galois orbits, enhancing existing theories.
Focus on special subvarieties of PEL types III and IV indicates unique behaviors in their arithmetic structure, contributing to the understanding of algebraic geometry dynamics.
This work builds on previous research, specifically Daw and Orr's contributions towards understanding interactions between lattices and skew-Hermitian forms.

Abstract

We prove the Zilber-Pink conjecture to the intersection of an irreducible Hodge generic algebraic subvariety V Ag with special subvarieties of all simple PEL types other than 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.

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Cite This Study

Bijay Raj Bhatta (Mon,) studied this question.

synapsesocial.com/papers/68e6494525bc5bdb98713977 https://doi.org/https://doi.org/10.48550/arxiv.2507.16827

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