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

Research output: Contribution to journalJournal articlepeer-review

  • Tobias Barthel

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.

Original languageEnglish
JournalAlgebras and Representation Theory
Volume20
Issue number3
Pages (from-to)569-581
Number of pages13
ISSN1386-923X
DOIs
Publication statusPublished - 1 Jun 2017

    Research areas

  • Auslander–Reiten theory, Brown–Comenetz duality, Generating hypothesis

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