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On higher torsion classes

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

Dokumenter

DOI

  • Javad Asadollahi, University of Isfahan
    • ,
  • Peter Jørgensen
  • Sibylle Schroll, University of Cologne
    • ,
  • Hipolito Treffinger, Sorbonne Université

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.

OriginalsprogEngelsk
TidsskriftNagoya Mathematical Journal
Vol/bind248
Sider (fra-til)823-848
ISSN0027-7630
DOI
StatusUdgivet - dec. 2022

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