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

作者：Barthel Tobias^*

来源：Algebras and Representation Theory, 2017, 20(3): 569-581.

DOI：10.1007/s10468-016-9655-y

• Auslander-Reiten theory
• Brown-Comenetz duality
• Generating hypothesis

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.

• 出版日期2017-6