Tobias Berger (University of Sheffield):

Deformations of Saito-Kurokawa type

Abstract: I will report on work in progress with Kris Klosin on the modularity of 4-dimensional symplectic representations whose reductions mod p are of Saito-Kurokawa type. This can be used to verify the paramodular conjecture of abelian surfaces over Q with a rational torsion point of order p in certain examples. I will also discuss the possibility of applying this to the modularity of elliptic curves over imaginary quadratic fields.

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