2016/03/30 by Tobias Barthel, Barthel, Tobias
Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1603.09181
openalex publication_date 2016/03/30 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
In this paper, we construct a version of Auslander-Reiten sequences for the\nK(n)-local stable homotopy category. In particular, the role of the\nAuslander-Reiten translation is played by the local Brown-Comenetz duality\nfunctor. As an application, we produce counterexamples to the K(n)-local\ngenerating hypothesis for all heights n>0 and all primes. Furthermore, our\nmethods apply to other triangulated categories, as for example the derived\ncategory of quasi-coherent sheaves on a smooth projective scheme.\n