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On Torsion Theories, Weight and t-Structures in Triangulated Categories. / Bondarko, M. V.; Vostokov, S. V.

In: Vestnik St. Petersburg University: Mathematics, Vol. 52, No. 1, 2019, p. 19-29.

Research output: Contribution to journal › Article › peer-review

Harvard

Bondarko, MV & Vostokov, SV 2019, 'On Torsion Theories, Weight and t-Structures in Triangulated Categories', Vestnik St. Petersburg University: Mathematics, vol. 52, no. 1, pp. 19-29. https://doi.org/10.3103/S1063454119010047

APA

Bondarko, M. V., & Vostokov, S. V. (2019). On Torsion Theories, Weight and t-Structures in Triangulated Categories. Vestnik St. Petersburg University: Mathematics, 52(1), 19-29. https://doi.org/10.3103/S1063454119010047

Vancouver

Bondarko MV, Vostokov SV. On Torsion Theories, Weight and t-Structures in Triangulated Categories. Vestnik St. Petersburg University: Mathematics. 2019;52(1):19-29. https://doi.org/10.3103/S1063454119010047

Author

Bondarko, M. V. ; Vostokov, S. V. / On Torsion Theories, Weight and t-Structures in Triangulated Categories. In: Vestnik St. Petersburg University: Mathematics. 2019 ; Vol. 52, No. 1. pp. 19-29.

BibTeX

@article{6f3ecfec2d1c4769a20f9b8eb96ab778,
title = "On Torsion Theories, Weight and t-Structures in Triangulated Categories",
abstract = "We study triangulated categories and torsion theories in them, and compare two definitions of torsion theories in this work. The most important types of torsion theories—weight structures and t-structures (and admissible triangulated subcategories) are also been considered. One of the aims of this paper is to show that a number of basic definitions and properties of weight and t-structures naturally extend to arbitrary torsion theories (in particular, we define smashing and cosmashing torsion theories). This can optimize some of the proofs. Similarly, the definitions of orthogonal and adjacent weight and t-structures are generalized. We relate the adjacency of torsion theories with Brown-Comenetz duality and Serre functors. These results may be applied to the study of t-structures in compactly generated triangulated categories and in derived categories of coherent sheaves. The relationship between torsion theories and projective classes is described.",
keywords = "adjacent structures, Brown-Comenetz duality, Serre functor, t-structures, torsion theories, triangulated categories, weight structures",
author = "Bondarko, {M. V.} and Vostokov, {S. V.}",
note = "Bondarko, M.V. & Vostokov, S.V. Vestnik St.Petersb. Univ.Math. (2019) 52: 19. https://doi.org/10.3103/S1063454119010047",
year = "2019",
doi = "10.3103/S1063454119010047",
language = "English",
volume = "52",
pages = "19--29",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "1",

}

RIS

TY - JOUR

T1 - On Torsion Theories, Weight and t-Structures in Triangulated Categories

AU - Bondarko, M. V.

AU - Vostokov, S. V.

N1 - Bondarko, M.V. & Vostokov, S.V. Vestnik St.Petersb. Univ.Math. (2019) 52: 19. https://doi.org/10.3103/S1063454119010047

PY - 2019

Y1 - 2019

N2 - We study triangulated categories and torsion theories in them, and compare two definitions of torsion theories in this work. The most important types of torsion theories—weight structures and t-structures (and admissible triangulated subcategories) are also been considered. One of the aims of this paper is to show that a number of basic definitions and properties of weight and t-structures naturally extend to arbitrary torsion theories (in particular, we define smashing and cosmashing torsion theories). This can optimize some of the proofs. Similarly, the definitions of orthogonal and adjacent weight and t-structures are generalized. We relate the adjacency of torsion theories with Brown-Comenetz duality and Serre functors. These results may be applied to the study of t-structures in compactly generated triangulated categories and in derived categories of coherent sheaves. The relationship between torsion theories and projective classes is described.

AB - We study triangulated categories and torsion theories in them, and compare two definitions of torsion theories in this work. The most important types of torsion theories—weight structures and t-structures (and admissible triangulated subcategories) are also been considered. One of the aims of this paper is to show that a number of basic definitions and properties of weight and t-structures naturally extend to arbitrary torsion theories (in particular, we define smashing and cosmashing torsion theories). This can optimize some of the proofs. Similarly, the definitions of orthogonal and adjacent weight and t-structures are generalized. We relate the adjacency of torsion theories with Brown-Comenetz duality and Serre functors. These results may be applied to the study of t-structures in compactly generated triangulated categories and in derived categories of coherent sheaves. The relationship between torsion theories and projective classes is described.

KW - adjacent structures

KW - Brown-Comenetz duality

KW - Serre functor

KW - t-structures

KW - torsion theories

KW - triangulated categories

KW - weight structures

UR - http://www.scopus.com/inward/record.url?scp=85064899937&partnerID=8YFLogxK

UR - https://link.springer.com/article/10.3103/S1063454119010047

U2 - 10.3103/S1063454119010047

DO - 10.3103/S1063454119010047

M3 - Article

AN - SCOPUS:85064899937

VL - 52

SP - 19

EP - 29

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -

ID: 49812411