2012/01/31 by Marc Levine · 1 citation
Mathematics · #math.AG #math.AT #msc:14C25 #msc:19E15 #msc:19E08 #msc:14F42 #msc:55P42
paper · pdf · doi:10.1112/jtopol/jtt031
4th version adds some remarks on combinatorial model categories,, makes some corrections to the appendix on symmetric products, corrects typos updates references
arxiv created 2013/03/07 · arxiv updated 2014/02/26
Let k be an algebraically closed field of characteristic zero. Let SH(k) denote the motivic stable homotopy category of T-spectra over k and SH the classical stable homotopy category. Let c:SH -> SH(k) be the functor induced by sending a space to the constant presheaf of spaces on Sm/k. We show that c is fully faithful. In particular, c induces an isomorphism πn(E)-> πn,0c(E) for all spectra E. Fix an embedding of k into the complex numbers and let Re:SH(k) -> SH be the associated Betti realization. We show that the slice tower for the motivic sphere spectrum has Betti realization which is strongly convergent. This gives a spectral sequence "of motivic origin" converging to the homotopy groups of the classical sphere spectrum; this spectral sequence at E2 agrees with the E2 terms in the Adams-Novikov spectral sequence.