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In this paper, we construct a version of Auslander–Reiten sequences for the ()-local stable homotopy category. In particular, the role of the Auslander–Reiten translation is played by the local Brown–Comenetz duality functor. As an application, we produce counterexamples to the ()-local generating hypothesis for all heights  > 0 and all primes. Furthermore, our methods apply to other triangulated categories, as for example the derived category of quasi-coherent sheaves on a smooth projective scheme.

Auslander–Reiten Sequences, Brown–Comenetz Duality, and the K(n)-local Generating Hypothesis