Modularity of abelian surfaces

Abstract: The paramodular conjecture states a relation between rational abelian surfaces (without extra endomorphisms) and some siegel modular forms. It is a generalization of the 1-dimensional case, namely the Shimura-Taniyama conjecture. In this talk I will explain the conjecture, its relation to modularity of elliptic curves over quadratic fields, the state of the art of the conjecture and some mention some proven cases. If time allows, I will present a Bianchi newform over Q(\sqrt{-7}) with rational eigenvalues which is attached to an abelian surface over Q( √ −7) (and explain its relation with the conjecture).

algebraic geometryalgebraic topologygroup theorynumber theoryrepresentation theory

Audience: researchers in the discipline

Queen Mary University of London Algebra and Number Theory Seminar