Group schemes and motivic spectra

Abstract

By a theorem of Mandell, May, Schwede and Shipley [21] the stable homotopy theory of classical S1-spectra is recovered from orthogonal spectra. In this paper general linear, special linear, symplectic, orthogonal and special orthogonal motivic spectra are introduced and studied. It is shown that stable homotopy theory of motivic spectra is recovered from each of these types of spectra. An application is given for the localization functor C∗ℱr:SHnis(k)→SHnis(k)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${C *}{\\cal F}r:{\\rm{S}}{{\\rm{H}}_{{\\rm{nis}}}}(k) \ o {\\rm{S}}{{\\rm{H}}_{{\\rm{nis}}}}(k)$$\\end{document} in the sense of [15] that converts Morel–Voevodsky stable motivic homotopy theory SH(k) into the equivalent local theory of framed bispectra [15].