Entanglement (Morlet Chair – Peter Stevenhagen )

Number fields arising by adjoining torsion points and radicals of points of coprime orders on an elliptic curve are generically  « independent », in the sense that the Galois group corresponding to the maximal radical extension satisfies an open image theorem in some generic group. Determining the exact entanglement of elliptic Kummer extensions is a currently arising field of study. We plan to consider this subject also for abelian varieties of higher dimension, and for modular and automorphic forms.