EVENT DETAILS AND ABSTRACT

Title: On descending cohomology geometrically
Speaker: Jeff Achter
Speaker Info: Colorado State University
Brief Description:
Special Note:
Abstract:

Mazur has drawn attention to the question of determining when the cohomology of a smooth, projective variety over a number field can be modeled by an abelian variety. I will discuss recent work with Casalaina-Martin and Vial which constructs such a "phantom" abelian variety for varieties with maximal geometric convieau. In the special case of cohomology in degree three, we show that the image of the (complex) Abel-Jacobi map admits a distinguished model over the base field, and that an algebraic correspondence realizes this descended intermediate Jacobian as a phantom.