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Hodge loci and atypical intersections: conjectures

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arxiv 1711.09387 v1 pith:7TZ6ULPD submitted 2017-11-26 math.AG

Bruno Klingler This is my paper · ORCID
classification math.AG
keywords conjecturehodgemixedadmissibleandratypicalbasecomplex
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We present a conjecture on the geometry of the Hodge locus of a (graded polarizable, admissible) variation of mixed Hodge structure over a complex smooth quasi-projective base, generalizing to this context the Zilber-Pink Conjecture for mixed Shimura varieties (in particular the Andr\'e-Oort conjecture).

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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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