summer 2018 



Davide Lombardo, Università di Pisa 10.05.2023 12:00, B137 Title: Families of Jacobians with quaternionic multiplication Abstract:
In joint work with Victoria Cantoral Farfán and John Voight we investigate families of evendimensional Jacobians defined over Q and admitting an action of the quaternion group. Such abelian varieties are unusual in several ways: for example, their ring of algebraic cycles is not generated by divisor classes, a fact which has consequences both on their arithmetic and on their geometry. We prove that  for every even dimension greater than two  100% of the members of the families we consider satisfy the Hodge, Tate and MumfordTate conjectures, compute their endomorphism rings, and provide explicit generators for their Hodge rings. As a consequence, we show that for such abelian varieties A the minimal field of definition of the endomorphisms and the minimal field over which the Galois representations attached to A have connected image are different. 

Last modified: 16.11.2022 