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.

In: Algebras and Representation Theory, Vol. 20, No. 3, 01.06.2017, p. 569-581.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Barthel, T 2017, 'Auslander–Reiten Sequences, Brown–Comenetz Duality, and the K(n)-local Generating Hypothesis', Algebras and Representation Theory, vol. 20, no. 3, pp. 569-581. https://doi.org/10.1007/s10468-016-9655-y

APA

Barthel, T. (2017). Auslander–Reiten Sequences, Brown–Comenetz Duality, and the K(n)-local Generating Hypothesis. Algebras and Representation Theory, 20(3), 569-581. https://doi.org/10.1007/s10468-016-9655-y

Vancouver

Barthel T. Auslander–Reiten Sequences, Brown–Comenetz Duality, and the K(n)-local Generating Hypothesis. Algebras and Representation Theory. 2017 Jun 1;20(3):569-581. https://doi.org/10.1007/s10468-016-9655-y

Author

Barthel, Tobias. / Auslander–Reiten Sequences, Brown–Comenetz Duality, and the K(n)-local Generating Hypothesis. In: Algebras and Representation Theory. 2017 ; Vol. 20, No. 3. pp. 569-581.

Bibtex

@article{1e658f82417343e4bbb6914a58fc4b54,
title = "Auslander–Reiten Sequences, Brown–Comenetz Duality, and the K(n)-local Generating Hypothesis",
abstract = "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.",
keywords = "Auslander–Reiten theory, Brown–Comenetz duality, Generating hypothesis",
author = "Tobias Barthel",
year = "2017",
month = jun,
day = "1",
doi = "10.1007/s10468-016-9655-y",
language = "English",
volume = "20",
pages = "569--581",
journal = "Algebras and Representation Theory",
issn = "1386-923X",
publisher = "Springer",
number = "3",

}

RIS

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