Chabert–Halberstadt's pre-Pólya group conjecture for A5-fields

Let $K$ be an $A_5$-field. The pre-Pólya group $\operatorname{Po}(K)_{nr}$ is the subgroup of $\operatorname{Cl}(K)$ generated by the classes of Ostrowski ideals above unramified primes.

Chabert–Halberstadt's conjecture.

$$\operatorname{Po}(K)_{nr}=\operatorname{Po}(K).$$

The conjecture concerns whether the pre-Pólya group already equals the Pólya group for every $A_5$-field. It is presented as an analogue of the preceding result for groups other than the exceptional cases, and its resolution is not indicated in the source.