  This note is the sequel to [A note on secondary K-theory. Algebra and Number
Theory 10 (2016), no. 4, 887-906]. Making use of the recent theory of
noncommutative motives, we prove that the canonical map from the derived Brauer
group to the secondary Grothendieck ring has the following injectivity
properties: in the case of a regular integral quasi-compact quasi-separated
scheme, it is injective; in the case of an integral normal Noetherian scheme
with a single isolated singularity, it distinguishes any two derived Brauer
classes whose difference is of infinite order. As an application, we show that
the canonical map is injective in the case of affine cones over smooth
projective plane complex curves of degree greater than or equal to four as well
as in the case of Mumford's (celebrated) singular surface.
