Unlikely intersections in families of abelian varieties.

Fabrizio Barroero (University of Basel)

Frank Adams 1,

Two varieties whose dimensions do not sum up to at least the dimension of the ambient space should not intersect. This is the guiding philosophy that led several authors to propose conjectures about subvarieties of commutative algebraic groups and of Shimura varieties. After a brief historic introduction we will talk about results for curves in families of abelian varieties, mostly obtained in collaboration with Laura Capuano.

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