The Zilber-Pink conjecture for varieties not defined over \mathbb Q

2025/04/01 by Bruno Klingler, Klingler, Bruno, Salim Tayou +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2504.00865

openalex publication_date 2025/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we prove the Zilber--Pink conjecture for subvarieties of mixed Shimura varieties, which are not defined over~\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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