Finiteness conjecture for optimal subvarieties in mixed Shimura varieties
Finiteness conjecture for optimal subvarieties in mixed Shimura varieties
Let be a mixed Shimura variety, let be a subvariety, and let denote the defect of a subvariety , where is the smallest special subvariety containing it. A subvariety is optimal if it is maximal for its defect: whenever and , one has . Finiteness conjecture for optimal subvarieties. For every subvariety , there are only finitely many optimal subvarieties. This is presented as formally equivalent to the strongest form of the Zilber–Pink conjecture for mixed Shimura varieties, but its status is not specified in the source.
Sources & referencesView supporting material
Primary source
Jonathan Pila and Jacob Tsimerman, “Independence of CM points in Elliptic Curves”, arXiv:1907.02737 (2019).
Additional references
2 papers in this index state this conjecture (2019). The statement above is taken from the most recent of them; the others are arXiv:1905.00827.
Progress summary
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