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Distinguished models of intermediate Jacobians

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Number theory; Algebraic geometry; Arithmetic number theory

video/mp4

Author affiliation: Colorado State University

2017-11-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63747

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/