A local-global principle for divisibility of points

In this talk I will present a Hasse principle for divisibility of rational points in algebraic groups, introduced by Dvornicich and Zannier in 2001, and motivated by a particular case of the Hasse principle on quadratic forms and by the Grunwald-Wang Theorem. I will give an overview on what is known so far and what answers are still missing. I will also link this question to other interesting problems, for example on torsion points on abelian varieties.

This is based on joint works with Laura Paladino, Rocco Chirivì, and Nirvana Coppola.