Abstract Charles Vial

Distinguished models of intermediate Jacobians

Abstract: Let X be a smooth projective variety defined over a subfield K of the complex numbers. It is natural to ask whether the complex abelian variety that is the image of the Abel-Jacobi map defined on algebraically trivial cycles admits a model over K. I will show that it admits a unique model making the Abel-Jacobi map equivariant with respect to the action of the automorphism group of the complex numbers fixing K. As an application, we answer a question of Mazur by showing that this model over the base field K is dominated by the Albanese variety of a product of components of the Hilbert scheme of X. We also recover a result of Deligne on complete intersections of Hodge level one. This is joint work with Jeff Achter and Yano Casalaina-Martin.