title: On torsion theories, weight and t-structures in triangulated categories
metadata.name: dc.contributor.author
metadata.value: Bondarko, Mikhail V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Vostokov, Sergey V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-05-24T07:57:03Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-05-24T07:57:03Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Bondarko M.V., Vostokov S.V. On torsion theories, weight and t-structures in triangulated categories. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 1, pp. 27–43.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.102
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15535
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The paper is dedicated to triangulated categories along with torsion theories in them; we compare two possible deﬁnitions of this notion. We also study the most important types of torsion theories, these being weight structures and t-structures (along with admissible triangulated subcategories). One of the main goals of the paper is to demonstrate that several important deﬁnitions and properties of weight structures and t-structures naturally extend to general torsion theories (so, we deﬁne smashing and cosmashing torsion theories); this observation leads to a certain optimization of proofs. Similarly we generalize the notion of adjacent and orthogonal weight and t-structures. Moreover, we relate adjacent torsion theories to the Brown-Comenetz duality and Serre functions; we hope to apply these results to the study of t-structures in compactly generated categories and in certain derived categories of coherent sheaves. Furthermore, we prove some completely new statements on the behaviour of torsion theories under exact functors. Lastly, we describe the relation of torsion theories to projective classes.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РНФ (грант № 16-11-10200).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 6 (64); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: triangulated categories
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: torsion theories
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: weight structures
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: t-structures
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: adjacent structures
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Brown—Comenetz duality
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Serre functor
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On torsion theories, weight and t-structures in triangulated categories
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 27-43.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15535/1/27-43.pdf
resources.format: Adobe PDF
resources.size: 355,64 kB