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On higher torsion classes

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Standard

On higher torsion classes. / Asadollahi, Javad; Jørgensen, Peter; Schroll, Sibylle et al.
I: Nagoya Mathematical Journal, Bind 248, 12.2022, s. 823-848.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Harvard

Asadollahi, J, Jørgensen, P, Schroll, S & Treffinger, H 2022, 'On higher torsion classes', Nagoya Mathematical Journal, bind 248, s. 823-848. https://doi.org/10.1017/nmj.2022.8

APA

Asadollahi, J., Jørgensen, P., Schroll, S., & Treffinger, H. (2022). On higher torsion classes. Nagoya Mathematical Journal, 248, 823-848. https://doi.org/10.1017/nmj.2022.8

CBE

Asadollahi J, Jørgensen P, Schroll S, Treffinger H. 2022. On higher torsion classes. Nagoya Mathematical Journal. 248:823-848. https://doi.org/10.1017/nmj.2022.8

MLA

Asadollahi, Javad et al. "On higher torsion classes". Nagoya Mathematical Journal. 2022, 248. 823-848. https://doi.org/10.1017/nmj.2022.8

Vancouver

Asadollahi J, Jørgensen P, Schroll S, Treffinger H. On higher torsion classes. Nagoya Mathematical Journal. 2022 dec.;248:823-848. doi: 10.1017/nmj.2022.8

Author

Asadollahi, Javad ; Jørgensen, Peter ; Schroll, Sibylle et al. / On higher torsion classes. I: Nagoya Mathematical Journal. 2022 ; Bind 248. s. 823-848.

Bibtex

@article{3aee97a7ff62445b8f18a05fe43be2bd,
title = "On higher torsion classes",
abstract = "Building on the embedding of an n-abelian category M into an abelian category A as an n-cluster-tilting subcategory of A, in this paper, we relate the n-torsion classes of M with the torsion classes of A. Indeed, we show that every n-torsion class in M is given by the intersection of a torsion class in A with M. Moreover, we show that every chain of n-torsion classes in the n-abelian category M induces a Harder–Narasimhan filtration for every object of M. We use the relation between M and A to show that every Harder–Narasimhan filtration induced by a chain of n-torsion classes in M can be induced by a chain of torsion classes in A. Furthermore, we show that n-torsion classes are preserved by Galois covering functors, thus we provide a way to systematically construct new (chains of) n-torsion classes.",
author = "Javad Asadollahi and Peter J{\o}rgensen and Sibylle Schroll and Hipolito Treffinger",
note = "Publisher Copyright: {\textcopyright} (2022) The Authors.",
year = "2022",
month = dec,
doi = "10.1017/nmj.2022.8",
language = "English",
volume = "248",
pages = "823--848",
journal = "Nagoya Mathematical Journal",
issn = "0027-7630",
publisher = "Cambridge University Press",

}

RIS

TY - JOUR

T1 - On higher torsion classes

AU - Asadollahi, Javad

AU - Jørgensen, Peter

AU - Schroll, Sibylle

AU - Treffinger, Hipolito

N1 - Publisher Copyright: © (2022) The Authors.

PY - 2022/12

Y1 - 2022/12

N2 - Building on the embedding of an n-abelian category M into an abelian category A as an n-cluster-tilting subcategory of A, in this paper, we relate the n-torsion classes of M with the torsion classes of A. Indeed, we show that every n-torsion class in M is given by the intersection of a torsion class in A with M. Moreover, we show that every chain of n-torsion classes in the n-abelian category M induces a Harder–Narasimhan filtration for every object of M. We use the relation between M and A to show that every Harder–Narasimhan filtration induced by a chain of n-torsion classes in M can be induced by a chain of torsion classes in A. Furthermore, we show that n-torsion classes are preserved by Galois covering functors, thus we provide a way to systematically construct new (chains of) n-torsion classes.

AB - Building on the embedding of an n-abelian category M into an abelian category A as an n-cluster-tilting subcategory of A, in this paper, we relate the n-torsion classes of M with the torsion classes of A. Indeed, we show that every n-torsion class in M is given by the intersection of a torsion class in A with M. Moreover, we show that every chain of n-torsion classes in the n-abelian category M induces a Harder–Narasimhan filtration for every object of M. We use the relation between M and A to show that every Harder–Narasimhan filtration induced by a chain of n-torsion classes in M can be induced by a chain of torsion classes in A. Furthermore, we show that n-torsion classes are preserved by Galois covering functors, thus we provide a way to systematically construct new (chains of) n-torsion classes.

U2 - 10.1017/nmj.2022.8

DO - 10.1017/nmj.2022.8

M3 - Journal article

AN - SCOPUS:85142092898

VL - 248

SP - 823

EP - 848

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

SN - 0027-7630

ER -