Periods and Selmer groups associated to mod p Galois representations over imaginary quadratic fields

We develop methods for computing arithmetic invariants associated to mod p Galois representations over imaginary quadratic fields. These invariants (period polynomials, Selmer groups) are conjectured to fit into the classical landscape of the Langlands program in analogous ways. In particular, the vanishing of coefficient(s) of the period polynomial should capture the non-vanishing of an associated Selmer group.