  For quantum Hamiltonian reductions in arbitrary characteristics, it is known
that derived localization holds if and only if the algebra of global sections
has finite global dimension. In this paper we provide an alternative
characterization of when derived localization holds: Derived localization holds
if and only if it holds for an explicit finite set of (quantized) line bundles.
As an application, we prove a new result that there are integral weights for
which localization holds on in the positive characteristic hypertoric case for
$p$ larger than an explicit bound. We also discuss how derived localization is
a consequence of a finite number of Morita equivalences.
