  The split property expresses the way in which local regions of spacetime
define subsystems of a quantum field theory. It is known to hold for general
theories in Minkowski space under the hypothesis of nuclearity. Here, the split
property is discussed for general locally covariant quantum field theories in
arbitrary globally hyperbolic curved spacetimes, using a spacetime deformation
argument to transport the split property from one spacetime to another. It is
also shown how states obeying both the split and (partial) Reeh-Schlieder
properties can be constructed, providing standard split inclusions of certain
local von Neumann algebras. Sufficient conditions are given for the theory to
admit such states in ultrastatic spacetimes, from which the general case
follows. A number of consequences are described, including the existence of
local generators for global gauge transformations, and the classification of
certain local von Neumann algebras. Similar arguments are applied to the distal
split property and circumstances are exhibited under which distal splitting
implies the full split property.
