  In the Dirac-Weyl equation that describes massless neutrino propagation in
the minimal Standard Model, the ($2\times 2$ equivalence of the) gamma matrices
convert Weyl spinors into spacetime tensors, and vice versa. They can thus be
regarded as amalgamations of three different types of mappings, one that
connects particle spinors directly forming representations to internal gauge
symmetries to their spacetime counterparts that are embodied by null flags,
another that translates the spacetime spinors into their corresponding tensors
expressed in an orthonormal tetrad, and finally a purely tensorial
transformation into the coordinate tetrad. The splitting of spinors into
particle and spacetime varieties is not usually practised, but we advocate its
adoption for better physical clarity, in terms of distinguishing internal and
spacetime transformations, and also for understanding the scattering of
neutrinos by spacetime curvature. We construct the basic infrastructure
required for this task, and provide a worked example for the Schwarzschild
spacetime. Our investigation also uncovers a possible under-determinacy in the
flavoured Dirac-Weyl equation, which could serve as a new incision point for
introducing flavour oscillation mechanisms.
