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