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O-minimality and certain atypical intersections

Abstract:

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 Andr\'e-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 def...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Authors


Habegger, P More by this author
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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Institute
Publisher:
Société Mathématique de France Publisher's website
Journal:
Annales scientifiques de l'ENS Journal website
Volume:
49
Issue:
4
Pages:
813-858
Publication date:
2016-07-05
Acceptance date:
2015-05-25
ISSN:
0012-9593
URN:
uuid:caf6b366-e63a-492d-a0bb-901e8ab8fa1b
Source identifiers:
483872
Local pid:
pubs:483872
Keywords:

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