Distinguished models of intermediate Jacobians

Jeff Achter
Thu, Feb 9, 2017
Colorado State University
PIMS CRG in Explicit Methods for Abelian Varieties
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. (This is joint work with Sebastian Casalaina-Martin and Charles Vial.) See the event webpage for more details.