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

TY - JOUR

T1 - Auslander–Reiten Sequences, Brown–Comenetz Duality, and the K(n)-local Generating Hypothesis

AU - Barthel, Tobias

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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.

AB - 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.

KW - Auslander–Reiten theory

KW - Brown–Comenetz duality

KW - Generating hypothesis

UR - http://www.scopus.com/inward/record.url?scp=84994726543&partnerID=8YFLogxK

U2 - 10.1007/s10468-016-9655-y

DO - 10.1007/s10468-016-9655-y

M3 - Journal article

AN - SCOPUS:84994726543

SN - 1386-923X

VL - 20

SP - 569

EP - 581

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

IS - 3

ER -