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DEGENERATING 0 IN TRIANGULATED CATEGORIES

Part of: Commutative algebra: Homological methods Homological methods

Published online by Cambridge University Press:  08 June 2020

MANUEL SAORÍN Open the ORCID record for MANUEL SAORÍN [Opens in a new window]  and
ALEXANDER ZIMMERMANN Open the ORCID record for ALEXANDER ZIMMERMANN [Opens in a new window]
MANUEL SAORÍN
Affiliation:
Departemento de Matemáticas, Universidad de Murcia, Aptdo. 4021, 30100 Espinardo, Murcia, Spain email [email protected]
ALEXANDER ZIMMERMANN
Affiliation:
Université de Picardie, Département de Mathématiques et LAMFA (UMR 7352 du CNRS), 33 rue St Leu, F-80039 Amiens Cedex 1, France email [email protected]
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Abstract

In previous work, based on the work of Zwara and Yoshino, we defined and studied degenerations of objects in triangulated categories analogous to the degeneration of modules. In triangulated categories ${\mathcal{T}}$, it is surprising that the zero object may degenerate. We show that the triangulated subcategory of ${\mathcal{T}}$ generated by the objects that are degenerations of zero coincides with the triangulated subcategory of ${\mathcal{T}}$ consisting of the objects with a vanishing image in the Grothendieck group $K_{0}({\mathcal{T}})$ of ${\mathcal{T}}$.

MSC classification

Primary: 16E35: Derived categories 13D09: Derived categories
Type
Article
Information
Nagoya Mathematical Journal , Volume 244 , December 2021 , pp. 158 - 167
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Copyright
© 2020 Foundation Nagoya Mathematical Journal

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Footnotes

The first named author was supported by research projects of the Ministerio de Economía y Competitividad of Spain (MTM2016-77445-P) and the Fundación ‘Séneca’ of Murcia (19880/GERM/15), both with a part of FEDER funds.

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