A survey of unlikely intersections in pure Shimura varieties, covering Andre-Oort, Andre-Pink-Zannier, Zilber-Pink, and the Pila-Zannier strategy.
Special points and Poincar\'e bi-extensions, with an Appendix by Bas Edixhoven
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abstract
The paper gives a counter-example to the relative version of the Manin-Mumford conjecture.
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Unlikely intersections in Shimura varieties and beyond: a survey
A survey of unlikely intersections in pure Shimura varieties, covering Andre-Oort, Andre-Pink-Zannier, Zilber-Pink, and the Pila-Zannier strategy.