3 problems

Chabert–Halberstadt's conjecture. If $h_K=2$, then

Mayer's conjecture. Non-Galois totally real cubic fields with these properties should exist in each of the following situations: type $\alpha_1$ with…

Scholz's conjecture. There should exist such fields $L$ for which either $f=1$, $\varrho_3(K)=2$, the complete $3$-elementary class group of $K$ capitulates in $N$, and $U_N=U_0$,…