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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
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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