Families of Jacobians with quaternionic multiplication

Davide Lombardo
Universitá di Pisa

Date(s) : 19/01/2023   iCal
11 h 00 min - 12 h 00 min

In joint work with Victoria Cantoral-Farfán and John Voight we investigate explicit families of even-dimensional Jacobians defined over Q and admitting an action of the quaternion group. These abelian varieties are unusual in several ways: for example, the ring of their algebraic cycles is not generated by divisor classes, a fact which has consequences both on their arithmetic and on their geometry.

We prove that 100% of the members of the families we consider satisfy the Hodge, Tate and Mumford-Tate conjectures, and provide explicit generators for their Hodge rings. As a consequence, we show that, for every even dimension greater than 2, there exist infinitely many abelian varieties A such that 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.

Rendez-vous à côté de la machine à café au rez-de-chaussée de l’ancienne BU.

Campus de Luminy, Marseille


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