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arXiv · 1909.01271

On the Zilber-Pink conjecture for complex abelian varieties

Fabrizio Barroero·Gabriel Andreas Dill
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Abstract

In this article, we prove that the Zilber-Pink conjecture for abelian varieties over an arbitrary field of characteristic $0$ is implied by the same statement for abelian varieties over the algebraic numbers. More precisely, the conjecture holds for subvarieties of dimension at most $m$ in the abelian variety $A$ if it holds for subvarieties of dimension at most $m$ in the largest abelian subvariety of $A$ that is isomorphic to an abelian variety defined over $\bar{ \mathbb{Q}}$.

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Fabrizio Barroero, Gabriel Andreas Dill. 2019-09-03. On the Zilber-Pink conjecture for complex abelian varieties. https://arxiv.org/abs/1909.01271

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