Standard

On weight complexes, pure functors, and detecting weights. / Bondarko, Mikhail V.

в: Journal of Algebra, Том 574, 15.05.2021, стр. 617-668.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Bondarko, MV 2021, 'On weight complexes, pure functors, and detecting weights', Journal of Algebra, Том. 574, стр. 617-668. https://doi.org/10.1016/j.jalgebra.2021.02.005

APA

Bondarko, M. V. (2021). On weight complexes, pure functors, and detecting weights. Journal of Algebra, 574, 617-668. https://doi.org/10.1016/j.jalgebra.2021.02.005

Vancouver

Bondarko MV. On weight complexes, pure functors, and detecting weights. Journal of Algebra. 2021 Май 15;574:617-668. https://doi.org/10.1016/j.jalgebra.2021.02.005

Author

Bondarko, Mikhail V. / On weight complexes, pure functors, and detecting weights. в: Journal of Algebra. 2021 ; Том 574. стр. 617-668.

BibTeX

@article{a78850da33fc41fa86cd2def0f22d29f,
title = "On weight complexes, pure functors, and detecting weights",
abstract = "This paper is dedicated to the study of weight complex functors (defined on triangulated categories endowed with weight structures) and their applications. We introduce pure (co)homological functors that “ignore all non-zero weights”; these have a nice description in terms of weight complexes. An important example is the weight structure wG generated by the orbit category in the G-equivariant stable homotopy category SH(G); the corresponding pure cohomological functors into abelian groups are the Bredon cohomology associated to Mackey functors ones. Pure functors related to “motivic” weight structures are also quite useful. Our results also give some (more) new weight structures. Moreover, we prove that certain exact functors are conservative and “detect weights”.",
keywords = "Bredon cohomology, Conservativity, Equivariant stable homotopy category, Mackey functors, Motives, Pure functors, Triangulated category, Weight complex, Weight structure, Weight-exact functor",
author = "Bondarko, {Mikhail V.}",
note = "Funding Information: Sections 1?4 were obtained under support of the Russian Science Foundation grant no. 16-11-00073. The work on Appendices A and B of the paper were supported by the Russian Science Foundation grant no. 20-41-04401. Publisher Copyright: {\textcopyright} 2021 Elsevier Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = may,
day = "15",
doi = "10.1016/j.jalgebra.2021.02.005",
language = "English",
volume = "574",
pages = "617--668",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - On weight complexes, pure functors, and detecting weights

AU - Bondarko, Mikhail V.

N1 - Funding Information: Sections 1?4 were obtained under support of the Russian Science Foundation grant no. 16-11-00073. The work on Appendices A and B of the paper were supported by the Russian Science Foundation grant no. 20-41-04401. Publisher Copyright: © 2021 Elsevier Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/5/15

Y1 - 2021/5/15

N2 - This paper is dedicated to the study of weight complex functors (defined on triangulated categories endowed with weight structures) and their applications. We introduce pure (co)homological functors that “ignore all non-zero weights”; these have a nice description in terms of weight complexes. An important example is the weight structure wG generated by the orbit category in the G-equivariant stable homotopy category SH(G); the corresponding pure cohomological functors into abelian groups are the Bredon cohomology associated to Mackey functors ones. Pure functors related to “motivic” weight structures are also quite useful. Our results also give some (more) new weight structures. Moreover, we prove that certain exact functors are conservative and “detect weights”.

AB - This paper is dedicated to the study of weight complex functors (defined on triangulated categories endowed with weight structures) and their applications. We introduce pure (co)homological functors that “ignore all non-zero weights”; these have a nice description in terms of weight complexes. An important example is the weight structure wG generated by the orbit category in the G-equivariant stable homotopy category SH(G); the corresponding pure cohomological functors into abelian groups are the Bredon cohomology associated to Mackey functors ones. Pure functors related to “motivic” weight structures are also quite useful. Our results also give some (more) new weight structures. Moreover, we prove that certain exact functors are conservative and “detect weights”.

KW - Bredon cohomology

KW - Conservativity

KW - Equivariant stable homotopy category

KW - Mackey functors

KW - Motives

KW - Pure functors

KW - Triangulated category

KW - Weight complex

KW - Weight structure

KW - Weight-exact functor

UR - http://www.scopus.com/inward/record.url?scp=85100908411&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2021.02.005

DO - 10.1016/j.jalgebra.2021.02.005

M3 - Article

AN - SCOPUS:85100908411

VL - 574

SP - 617

EP - 668

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

ID: 75128889