Chinburg's $\Omega(3)$ conjecture modulo the kernel group

Let $F/K$ be a finite Galois extension of number fields with Galois group $G$, let $\Cl(\Z[G])$ be the locally free class group, and let $\D(\Z[G])$ be the kernel of the map from $\Cl(\Z[G])$ to the locally free class group of a maximal order in $\Q[G]$. Let $\Omega(F/K,3)$ and $W_{F/K}$ be the classes defined from a Tate sequence and Artin root numbers, respectively.

Chinburg's $\Omega(3)$ conjecture modulo the kernel group.

$$\Omega(F/K,3)\equiv W_{F/K}\pmod{\D(\Z[G])}.$$

This is a weakening of Chinburg's $\Omega(3)$ conjecture obtained by passing to the quotient by the kernel subgroup. The supplied excerpt gives no general resolution, although it immediately records a special solved case when $F/\Q$ is abelian.