The Q-shaped derived category of a ring

Institut for Matematiske Fag

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The Q-shaped derived category of a ring. / Holm, Henrik; Jørgensen, Peter.

I: Journal of the London Mathematical Society, Bind 106, Nr. 4, 2022, s. 3263-3316.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Holm, H & Jørgensen, P 2022, 'The Q-shaped derived category of a ring', Journal of the London Mathematical Society, bind 106, nr. 4, s. 3263-3316. https://doi.org/10.1112/jlms.12662

APA

Holm, H., & Jørgensen, P. (2022). The Q-shaped derived category of a ring. Journal of the London Mathematical Society, 106(4), 3263-3316. https://doi.org/10.1112/jlms.12662

Vancouver

Holm H, Jørgensen P. The Q-shaped derived category of a ring. Journal of the London Mathematical Society. 2022;106(4):3263-3316. https://doi.org/10.1112/jlms.12662

Author

Holm, Henrik ; Jørgensen, Peter. / The Q-shaped derived category of a ring. I: Journal of the London Mathematical Society. 2022 ; Bind 106, Nr. 4. s. 3263-3316.

Bibtex

@article{4f33dff9e8e9449f9805b34c962c8c50,

title = "The Q-shaped derived category of a ring",

abstract = "For any ring (Formula presented.) and a small, pre-additive, Hom-finite, and locally bounded category (Formula presented.) that has a Serre functor and satisfies the (strong) retraction property, we show that the category of additive functors (Formula presented.) has a projective and an injective model structure. These model structures have the same trivial objects and weak equivalences, which in most cases can be naturally characterized in terms of certain (co)homology functors introduced in this paper. The associated homotopy category, which is triangulated, is called the (Formula presented.) -shaped derived category of (Formula presented.). The usual derived category of (Formula presented.) is one example; more general examples arise by taking (Formula presented.) to be the mesh category of a suitably nice stable translation quiver. This paper builds upon, and generalizes, works of Enochs, Estrada, and Garc{\'i}a-Rozas (Math. Nachr. 281 (2008), no. 4, 525–540) and Dell'Ambrogio, Stevenson, and {\v S}{\v t}ov{\'i}{\v c}ek (Math. Z. 287 (2017), no. 3-4, 1109–1155).",

author = "Henrik Holm and Peter J{\o}rgensen",

note = "Publisher Copyright: {\textcopyright} 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.",

year = "2022",

doi = "10.1112/jlms.12662",

language = "English",

volume = "106",

pages = "3263--3316",

journal = "Journal of the London Mathematical Society",

issn = "0024-6107",

publisher = "Oxford University Press",

number = "4",

}

RIS

TY - JOUR

T1 - The Q-shaped derived category of a ring

AU - Holm, Henrik

AU - Jørgensen, Peter

PY - 2022

Y1 - 2022

N2 - For any ring (Formula presented.) and a small, pre-additive, Hom-finite, and locally bounded category (Formula presented.) that has a Serre functor and satisfies the (strong) retraction property, we show that the category of additive functors (Formula presented.) has a projective and an injective model structure. These model structures have the same trivial objects and weak equivalences, which in most cases can be naturally characterized in terms of certain (co)homology functors introduced in this paper. The associated homotopy category, which is triangulated, is called the (Formula presented.) -shaped derived category of (Formula presented.). The usual derived category of (Formula presented.) is one example; more general examples arise by taking (Formula presented.) to be the mesh category of a suitably nice stable translation quiver. This paper builds upon, and generalizes, works of Enochs, Estrada, and García-Rozas (Math. Nachr. 281 (2008), no. 4, 525–540) and Dell'Ambrogio, Stevenson, and Šťovíček (Math. Z. 287 (2017), no. 3-4, 1109–1155).

AB - For any ring (Formula presented.) and a small, pre-additive, Hom-finite, and locally bounded category (Formula presented.) that has a Serre functor and satisfies the (strong) retraction property, we show that the category of additive functors (Formula presented.) has a projective and an injective model structure. These model structures have the same trivial objects and weak equivalences, which in most cases can be naturally characterized in terms of certain (co)homology functors introduced in this paper. The associated homotopy category, which is triangulated, is called the (Formula presented.) -shaped derived category of (Formula presented.). The usual derived category of (Formula presented.) is one example; more general examples arise by taking (Formula presented.) to be the mesh category of a suitably nice stable translation quiver. This paper builds upon, and generalizes, works of Enochs, Estrada, and García-Rozas (Math. Nachr. 281 (2008), no. 4, 525–540) and Dell'Ambrogio, Stevenson, and Šťovíček (Math. Z. 287 (2017), no. 3-4, 1109–1155).

UR - http://www.scopus.com/inward/record.url?scp=85134175604&partnerID=8YFLogxK

U2 - 10.1112/jlms.12662

DO - 10.1112/jlms.12662

M3 - Journal article

AN - SCOPUS:85134175604

VL - 106

SP - 3263

EP - 3316

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 4

ER -

ID: 317817886