Number Theory seminar: Alexander Molnar

Title: Arithmetic on intermediate Jacobians of some rigid Calabi-Yau threefolds.

Speaker: Alexander Molnar, Queen's University, Kingston.

Abstract: Generalizing the Jacobian variety of a curve, one may associate to any higher dimensional complex variety X some (complex) varieties defined in terms of cohomological quotients of X, the intermediate Jacobians. These receive cycle class maps, so there is much interest in being able to define them over number fields in order to study the many open conjectures on cycles and Chow groups of varieties.

We will discuss some examples of rigid Calabi-Yau threefolds where we may compute the intermediate Jacobians as complex tori, and show that each model of the threefolds over the rational numbers leads to a natural rational model of the intermediate Jacobians. This allows us to consider (quadratic) twists of the threefolds, see how this affects the intermediate Jacobian, and compute the L-functions of the twisted threefolds and the respective twisted intermediate Jacobians, as well as their special values and look for links between them.