Auslander–Reiten Sequences, Brown–Comenetz Duality, and the K(n)-local Generating Hypothesis
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Auslander–Reiten Sequences, Brown–Comenetz Duality, and the K(n)-local Generating Hypothesis. / Barthel, Tobias.
I: Algebras and Representation Theory, Bind 20, Nr. 3, 01.06.2017, s. 569-581.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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
VL - 20
SP - 569
EP - 581
JO - Algebras and Representation Theory
JF - Algebras and Representation Theory
SN - 1386-923X
IS - 3
ER -
ID: 178793493