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O-minimality and certain atypical intersections
JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
 
ID 3248081
Author(s) Habegger, Philipp; Pila, Jonathan
Author(s) at UniBasel Habegger, Philipp
Year 2016
Year: comment Accepted for publication
Title O-minimality and certain atypical intersections
Journal Annales Scientifiques de l'École Normale Supérieure
Volume 49
Number 4
Pages / Article-Number 813-858
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 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.
Publisher Société Mathématique de France
ISSN/ISBN 0012-9593
URL http://smf4.emath.fr/Publications/AnnalesENS/4_49/html/ens_ann-sc_49_813-858.php
edoc-URL http://edoc.unibas.ch/51741/
Full Text on edoc No
Digital Object Identifier DOI 10.24033/asens.2296
ISI-Number WOS:000390294900002
Document type (ISI) Article
 
   

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