O-minimality and certain atypical intersections

Habegger, Philipp and Pila, Jonathan. (2016) O-minimality and certain atypical intersections. Annales Scientifiques de l'École Normale Supérieure, 49 (4). pp. 813-858.

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Official URL: http://edoc.unibas.ch/51741/

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We show that the strategy of point counting in o-minimal structures can be applied to various problems on unlikely intersections that go beyond the conjectures of Manin-Mumford and André-Oort. We verify the so-called Zilber-Pink Conjecture in a product of modular curves on assuming a lower bound for Galois orbits and a sufficiently strong modular Ax-Schanuel Conjecture. In the context of abelian varieties we obtain the Zilber-Pink Conjecture for curves unconditionally when everything is defined over a number field. For higher dimensional subvarieties of abelian varieties we obtain some weaker results and some conditional results.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Zahlentheorie (Habegger)
UniBasel Contributors:Habegger, Philipp
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Société Mathématique de France
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:25 Apr 2018 09:15
Deposited On:25 Apr 2018 09:15

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