Auslander-Reiten sequences, Brown-Comenetz duality, and the $K(n)$-local generating hypothesis
Algebraic Topology
2016-03-31 v1 Representation Theory
Abstract
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 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.
Keywords
Cite
@article{arxiv.1603.09181,
title = {Auslander-Reiten sequences, Brown-Comenetz duality, and the $K(n)$-local generating hypothesis},
author = {Tobias Barthel},
journal= {arXiv preprint arXiv:1603.09181},
year = {2016}
}