Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 767

Preprint Number 767

Previous Next Preprint server

767. Philipp Habegger and Jonathan Pila
O-minimality and certain atypical intersections

Submission date: 2 September 2014


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.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1409.0771: pdf, ps.

Last updated: March 23 2021 10:23 Please send your corrections to: