A note on unlikely intersections in Shimura varieties
Vahagn Aslanyan, Christopher Daw
TL;DR
This paper explores the connections between major conjectures in the theory of Shimura varieties and derives new results on unlikely intersections by combining these conjectures.
Contribution
It introduces new results on unlikely intersections in Shimura varieties by linking several prominent conjectures in the field.
Findings
New results on unlikely intersections in Shimura varieties
Connections established between André-Oort, André-Pink-Zannier, and Mordell-Lang conjectures
Combines geometric Zilber-Pink conjecture with other conjectures to derive results
Abstract
We discuss the relationships between the Andr\'e-Oort, Andr\'e-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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds