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

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Abstract

In this paper, we construct a version of Auslander–Reiten sequences for the K(n)-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 K(n)-local generating hypothesis for all heights n > 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.

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  1. Max Planck Institute for Mathematics, University of Copenhagen, Copenhagen, Denmark

    Tobias Barthel

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  1. Tobias Barthel
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Correspondence to Tobias Barthel.

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Presented by Henning Krause.

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Barthel, T. Auslander–Reiten Sequences, Brown–Comenetz Duality, and the K(n)-local Generating Hypothesis. Algebr Represent Theor 20, 569–581 (2017). https://doi.org/10.1007/s10468-016-9655-y

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  • DOI: https://doi.org/10.1007/s10468-016-9655-y

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