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In mathematics, the Zilber–Pink conjecture is a far-reaching generalisation of many famous Diophantine conjectures and statements, such as André–Oort, Manin–Mumford, and Mordell–Lang. For algebraic tori and semiabelian varieties it was proposed by Boris Zilber and independently by Enrico Bombieri, David Masser, Umberto Zannier in the early 2000's. For semiabelian varieties the conjecture implies the Mordell–Lang and Manin–Mumford conjectures. Richard Pink proposed (again independently) a more general conjecture for Shimura varieties which also implies the André–Oort conjecture. In the case of algebraic tori, Zilber called it the Conjecture on Intersection with Tori (CIT). The general version is now known as the Zilber–Pink conjecture. It states roughly that atypical or unlikely intersections of an algebraic variety with certain special varieties are accounted for by finitely many special varieties.
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References
- 1 2 3 4 "Curriculum Vitae" (PDF). Philipp Habegger. November 2010. Retrieved 5 March 2021.
- ↑ Philipp Habegger at the Mathematics Genealogy Project
- 1 2 "Philipp Habegger". Institute for Advanced Study . 9 December 2019. Retrieved 5 March 2021.
- ↑ "Philipp Habegger". University of Basel (in German). Retrieved 5 March 2021.
