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A model-independent, locally generally covariant formulation of quantum fieldtheory over four-dimensional, globally hyperbolic spacetimes will be givenwhich generalizes similar, previous approaches. Here, a generally covariantquantum field theory is an assignment of quantum fields to globally hyperbolicspacetimes with spin-structure where each quantum field propagates on thespacetime to which it is assigned. Imposing very natural conditions such aslocal general covariance, existence of a causal dynamical law, fixed spinor- ortensor-type for all quantum fields of the theory, and that the quantum field onMinkowski spacetime satisfies the usual conditions, it will be shown that aspin-statistics theorem hols: If for some spacetimes the corresponding quantumfield obeys the "wrong" connection between spin and statistics, then allquantum fields of the theory, on each spacetime, are trivial.Comment: latex2e, 1 figure, 32 page

A Spin-Statistics Theorem for Quantum Fields¶on Curved Spacetime Manifolds¶in a Generally Covariant Framework