Classically, governing fields were used to control the 2-power torsion in quadratic extensions. This talk will be about a new attempt to generalize the theory and try to control the 3-power torsion in cyclic cubic extensions instead. The goal of this work was initially to show that Z/9Z occurs in infinitely many class groups using no analysis stronger than the Cheboratev density theorem, which has recently been achieved. This is joint work with Abtien Javanpeykar and Peter Stevenhagen.