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In this paper, we construct a version of Auslander-Reiten sequences for the$K(n)$-local stable homotopy category. In particular, the role of theAuslander-Reiten translation is played by the local Brown-Comenetz dualityfunctor. As an application, we produce counterexamples to the $K(n)$-localgenerating hypothesis for all heights $n>0$ and all primes. Furthermore, ourmethods apply to other triangulated categories, as for example the derivedcategory of quasi-coherent sheaves on a smooth projective scheme.

Auslander-Reiten sequences, Brown-Comenetz duality, and the $K(n)$-local generating hypothesis