  A model-independent, locally generally covariant formulation of quantum field
theory over four-dimensional, globally hyperbolic spacetimes will be given
which generalizes similar, previous approaches. Here, a generally covariant
quantum field theory is an assignment of quantum fields to globally hyperbolic
spacetimes with spin-structure where each quantum field propagates on the
spacetime to which it is assigned. Imposing very natural conditions such as
local general covariance, existence of a causal dynamical law, fixed spinor- or
tensor-type for all quantum fields of the theory, and that the quantum field on
Minkowski spacetime satisfies the usual conditions, it will be shown that a
spin-statistics theorem hols: If for some spacetimes the corresponding quantum
field obeys the "wrong" connection between spin and statistics, then all
quantum fields of the theory, on each spacetime, are trivial.
