Seminar
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| Location: | SLMath: Online/Virtual |
To participate in this seminar, please register here: https://www.msri.org/seminars/25206
The seminar will feature research talks by distinguished researchers in a range of areas related to the program. The lectures will be delivered in the colloquium style and accessible to broad audience.
Unlikely Intersections In Families Of Abelian Varieties
To participate in this seminar, please register here: https://www.msri.org/seminars/25206
Abstract:
Manin Mumford conjecture about the distribution of torsion points on subvarieties of semiabelian varieties has a natural analogue in families, and one can formulate more general conjectures in this setting. I will treat the relative Manin-Mumford results proved by Masser and Zannier for curves in a one-parameter family of abelian varieties and more general results obtained in this setting in collaboration with F. Barroero. The proofs of these results uses a method introduced for the first time by Pila and Zannier who gave an alternative proof of Manin-Mumford conjecture; this is based on the combination of tools coming from the theory of o-minimality, in particular a theorem of Pila and Wilkie about counting rational points of bounded height on certain transcendental varieties with other Diophantine ingredients.
No Notes/Supplements UploadedUnlikely Intersections In Families Of Abelian Varieties
| H.264 Video | 25125_28623_8600_Unlikely_intersections_in_families_of_abelian_varieties.mp4 |