Number theory seminar

Speaker: Samuel Le Fourn (Grenoble)

Title: Growth of torsion groups of a fixed abelian variety over varying number fields.

Abstract: Fixing an abelian variety A over a number field K, the Mordell-Weil theorem implies that for every finite extension L/K, the
torsion group of A(L) is finite. The growth of this group is polynomial in [L:K], with an optimal exponent conjectured by Hindry and Ratazzi in 2012. In a joint work with Davide Lombardo and David Zywina, we prove that this conjecture is equivalent to the Mumford-Tate conjecture. I will explain in this talk parts of the proof, in particular how monodromy groups dictate the growth of the l-torsion for a prime l.