Group schemes and motivic spectra

2018/12/04 by Grigory Garkusha, Garkusha, Grigory
Mathematics · Medicine · #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Systemic Lupus Erythematosus Research

paper · pdf · doi:10.48550/arxiv.1812.01384

openalex publication_date 2018/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By a theorem of Mandell-May-Schwede-Shipley 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 the stable homotopy theory of motivic spectra is recovered from each of these types of spectra. An application is given for the localization functor C_*\mathcal Fr:SH_nis(k)→ SH_nis(k) in the sense of [15] that converts the Morel-Voevodsky stable motivic homotopy theory SH(k) into the equivalent local theory of framed bispectra [15].

Related

• Motivic stable homotopy groups
• Motivic homotopy theory and stable homotopy groups
• Motivic spectra and universality of K-theory
• Periodic phenomena in stable motivic homotopy theory
• Spectra and symmetric spectra in general model categories