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The Zilber-Pink conjecture for varieties not defined over $\overline{\mathbb Q}$

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arxiv 2504.00865 v1 pith:7YG2BYYH submitted 2025-04-01 math.AG math.NT

Bruno Klingler , Salim Tayou This is my paper · ORCID
classification math.AGmath.NT
keywords conjecturedefinedmathbbmixedoverlineprovevarietiesabsolute
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abstract

In this note, we prove the Zilber--Pink conjecture for subvarieties of mixed Shimura varieties, which are not defined over~$\overline{\mathbb Q}$ in a strong sense. We prove similar results for general variations of mixed Hodge structure of geometric origin, assuming furthermore that they are absolute.

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  1. Unlikely intersections in Shimura varieties and beyond: a survey

    math.NT 2025-06 accept

    A survey of unlikely intersections in pure Shimura varieties, covering Andre-Oort, Andre-Pink-Zannier, Zilber-Pink, and the Pila-Zannier strategy.

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