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 ΣP1X+, 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+.

Original languageEnglish
Article number106834
JournalJournal of Pure and Applied Algebra
Volume226
Issue number3
DOIs
StatePublished - 1 Mar 2022

    Scopus subject areas

  • Algebra and Number Theory

    Research areas

  • Fibrant resolutions, Framed motives, Moving lemmas, Stable motivic homotopy theory

ID: 98952217