A note on unlikely intersections in Shimura varieties

2022/09/16 by Vahagn Aslanyan, Aslanyan, Vahagn, Christopher Daw +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Logic (math.LO) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2209.07967

openalex publication_date 2022/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the relationships between the André-Oort, André-Pink-Zannier, and Mordell-Lang conjectures for Shimura varieties. We then combine the latter with the geometric Zilber-Pink conjecture to obtain some new results on unlikely intersections in Shimura varieties.

Cited by

• Modular Zilber-Pink for geometrically generic varieties
• Unlikely intersections in Shimura varieties and beyond: a survey

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• Generalised André-Pink-Zannier Conjecture for Shimura varieties of abelian type
• The Zilber-Pink conjecture for varieties not defined over \mathbb Q
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• Distinguished categories and the Zilber-Pink conjecture