Characterization and finite descent of local cohomological invariants

We provide simple ``left-inverse characterizations’’ of the recently introduced singularity invariants $c(Z)$, $w(Z)$, and $\mathrm{H}\mathrm{R}\mathrm{H}(Z)$ of an equidimensional variety $Z$. Combining this with a trace morphism, we establish descent results of these invariants for finite surjective morphisms.