Distinguished models of intermediate Jacobians

Consider a smooth projective variety over a number field. The image of the associated (complex) Abel-Jacobi map inside the (transcendental) intermediate Jacobian is a complex abelian variety. We show that this abelian variety admits a distinguished model over the original number field, and use it to address a problem of Mazur on modeling the cohomology of an arbitrary smooth projective variety by that of an abelian variety. (We also recover an old theorem of Deligne on intermediate Jacobians of complete intersection varieties.) In special cases, our construction gives a way to compare certain arithmetic moduli spaces to moduli spaces of abelian varieties. We expect that more such applications exist. This is joint work with Sebastian Casalaina-Martin and Charles Vial.Non UBCUnreviewedAuthor affiliation: Colorado State UniversityFacult