Standard

Framed motives of smooth affine pairs. / Druzhinin, A.

в: Journal of Pure and Applied Algebra, Том 226, № 3, 106834, 01.03.2022.

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

Harvard

Druzhinin, A 2022, 'Framed motives of smooth affine pairs', Journal of Pure and Applied Algebra, Том. 226, № 3, 106834. https://doi.org/10.1016/j.jpaa.2021.106834

APA

Druzhinin, A. (2022). Framed motives of smooth affine pairs. Journal of Pure and Applied Algebra, 226(3), [106834]. https://doi.org/10.1016/j.jpaa.2021.106834

Vancouver

Druzhinin A. Framed motives of smooth affine pairs. Journal of Pure and Applied Algebra. 2022 Март 1;226(3). 106834. https://doi.org/10.1016/j.jpaa.2021.106834

Author

Druzhinin, A. / Framed motives of smooth affine pairs. в: Journal of Pure and Applied Algebra. 2022 ; Том 226, № 3.

BibTeX

@article{f44d4d5457ab416da10f433e7e1218fb,
title = "Framed motives of smooth affine pairs",
abstract = "The theory of framed motives by Garkusha and Panin gives computations in the stable motivic homotopy category SH(k) in terms of Voevodsky's framed correspondences. In particular, the motivically fibrant Ω-resolution in positive degrees of the motivic suspension spectrum ΣP1∞X+, where X+=X⨿⁎, for a smooth scheme X∈Smk over an infinite perfect field k, is computed. The computation by Garkusha, Neshitov and Panin of the framed motives of relative motivic spheres (Al×X)/((Al−0)×X), X∈Smk, is one of ingredients in the theory. In the article we extend this result to the case of a pair (X,U) given by a smooth affine variety X over k and an open subscheme U⊂X. The result gives an explicit motivically fibrant Ω-resolution in positive degrees for the motivic suspension spectrum ΣP1∞(X+/U+) of the quotient-sheaf X+/U+.",
keywords = "Fibrant resolutions, Framed motives, Moving lemmas, Stable motivic homotopy theory",
author = "A. Druzhinin",
note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",
year = "2022",
month = mar,
day = "1",
doi = "10.1016/j.jpaa.2021.106834",
language = "English",
volume = "226",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier",
number = "3",

}

RIS

TY - JOUR

T1 - Framed motives of smooth affine pairs

AU - Druzhinin, A.

N1 - Publisher Copyright: © 2021 Elsevier B.V.

PY - 2022/3/1

Y1 - 2022/3/1

N2 - The theory of framed motives by Garkusha and Panin gives computations in the stable motivic homotopy category SH(k) in terms of Voevodsky's framed correspondences. In particular, the motivically fibrant Ω-resolution in positive degrees of the motivic suspension spectrum ΣP1∞X+, where X+=X⨿⁎, for a smooth scheme X∈Smk over an infinite perfect field k, is computed. The computation by Garkusha, Neshitov and Panin of the framed motives of relative motivic spheres (Al×X)/((Al−0)×X), X∈Smk, is one of ingredients in the theory. In the article we extend this result to the case of a pair (X,U) given by a smooth affine variety X over k and an open subscheme U⊂X. The result gives an explicit motivically fibrant Ω-resolution in positive degrees for the motivic suspension spectrum ΣP1∞(X+/U+) of the quotient-sheaf X+/U+.

AB - The theory of framed motives by Garkusha and Panin gives computations in the stable motivic homotopy category SH(k) in terms of Voevodsky's framed correspondences. In particular, the motivically fibrant Ω-resolution in positive degrees of the motivic suspension spectrum ΣP1∞X+, where X+=X⨿⁎, for a smooth scheme X∈Smk over an infinite perfect field k, is computed. The computation by Garkusha, Neshitov and Panin of the framed motives of relative motivic spheres (Al×X)/((Al−0)×X), X∈Smk, is one of ingredients in the theory. In the article we extend this result to the case of a pair (X,U) given by a smooth affine variety X over k and an open subscheme U⊂X. The result gives an explicit motivically fibrant Ω-resolution in positive degrees for the motivic suspension spectrum ΣP1∞(X+/U+) of the quotient-sheaf X+/U+.

KW - Fibrant resolutions

KW - Framed motives

KW - Moving lemmas

KW - Stable motivic homotopy theory

UR - http://www.scopus.com/inward/record.url?scp=85110658751&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/f6ad6743-a628-3cc2-8659-6a552c8d34c5/

U2 - 10.1016/j.jpaa.2021.106834

DO - 10.1016/j.jpaa.2021.106834

M3 - Article

AN - SCOPUS:85110658751

VL - 226

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 3

M1 - 106834

ER -

ID: 98952217