On higher torsion classes

Javad Asadollahi; Peter Jørgensen; Sibylle Schroll; Hipolito Treffinger

doi:10.1017/nmj.2022.8

On higher torsion classes

Javad Asadollahi, Peter Jørgensen, Sibylle Schroll, Hipolito Treffinger

Institut for Matematik

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

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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.

Originalsprog	Engelsk
Tidsskrift	Nagoya Mathematical Journal
Vol/bind	248
Sider (fra-til)	823-848
ISSN	0027-7630
DOI	https://doi.org/10.1017/nmj.2022.8
Status	Udgivet - dec. 2022

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10.1017/nmj.2022.8Licens: CC BY

on-higher-torsion-classesForlagets udgivne version, 516 KBLicens: CC BY

Citationsformater

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AU - Asadollahi, Javad

AU - Jørgensen, Peter

AU - Schroll, Sibylle

AU - Treffinger, Hipolito

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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

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SP - 823

EP - 848

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

ER -

On higher torsion classes

Abstract

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