The ETNC for abelian extensions of imaginary quadratic fields

The equivariant Tamagawa number conjecture (ETNC) on special values of L-functions is known in full for absolutely abelian fields from the work of Burns, Flach, and Greither. My work concerns the case of abelian extensions of imaginary quadratic fields. I have proved the conjecture at negative integral values of the L-function, while Bley has proved the conjecture at zero. Both of these results have some restrictions on primes. Removing these restrictions seems to involve proving the vanishing of the cyclotomic μ-invariant. I will sketch the proof of my result and discuss the prospect of a full proof of the conjecture.