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Seminar

DDC - Online Seminar: Unlikely intersections in families of abelian varieties October 29, 2020 (09:00 AM PDT - 10:00 AM PDT)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Laura Capuano (Politecnico di Torino)
Description

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.

Video

Unlikely Intersections In Families Of Abelian Varieties

Abstract/Media

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.

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Unlikely Intersections In Families Of Abelian Varieties

H.264 Video 25125_28623_8600_Unlikely_intersections_in_families_of_abelian_varieties.mp4