  We prove a generalization of the Hochster-Roberts-Boutot-Kawamata Theorem
conjectured by Aschenbrenner and the author: let $R\to S$ be a pure
homomorphism of equicharacteristic zero Noetherian local rings. If $S$ is
regular, then $R$ is pseudo-rational, and if $R$ is moreover $\mathbb
Q$-Gorenstein, then it pseudo-log-terminal.
