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- W4380994502 abstract "Let $X$ be a quasi projective scheme over a noetherian affine scheme $Spec(A)$, $Usubseteq X$ be an open subset, and $Z=X-U$. Consider the map $q:{mathbb K}left({mathscr V}(X)right) rightarrow {mathbb K}left({mathscr V} U)right)$ of the ${mathbb K}$-theory spectra. We give a description of the homotopy fiber of $q$. Let $C{mathbb M}^Zleft({mathscr V}(X) right)$ denote the full subcategory of ${mathscr F} in Coh(X)$ such that (1) ${mathscr F}_{|U}=0$, (2) $grade(Z, X)=grade({mathscr F} )=dim_{{mathscr V}(X)}{mathscr F} $. It turns out that the homotopy fiber of $q$ is the ${mathbb K}$-theory spectra ${mathbb K}left(C{mathbb M}^Zleft({mathscr V}(X) right)right)$. Likewise, we compute the homotopy fiber of the the pullback map $$g: {mathbb G}Wleft({mathscr V}(X)right) rightarrow {mathbb G}Wleft({mathscr V}(U)right)$$ of Grothendieck-Witt bispectra. Consequently, we obtain long exact sequences of ${mathbb K}$-groups and of ${mathbb G}W$-groups." @default.
- W4380994502 created "2023-06-17" @default.
- W4380994502 creator A5018156727 @default.
- W4380994502 date "2023-06-15" @default.
- W4380994502 modified "2023-09-26" @default.
- W4380994502 title "Fundamental Exact sequences in ${mathbb K}$-theory" @default.
- W4380994502 doi "https://doi.org/10.48550/arxiv.2306.09284" @default.
- W4380994502 hasPublicationYear "2023" @default.
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