2005/10/16 by Marc Levine · 2 citations
Mathematics · #math.AG #math.AT #msc:14C25 #msc:55P42 #msc:19E08 #msc:14F42
paper · pdf · doi:10.1112/jtopol/jtm004
A revised and extended version of an earlier paper, which is on the K-theory server
arxiv created 2005/10/16 · arxiv updated 2014/02/26
We examine the "homotopy coniveau tower" for a general cohomology theory on smooth k-schemes and give a new proof that the layers of this tower for K-theory agree with motivic cohomology. In addition, the homotopy coniveau tower agrees with Voevodsky's slice tower for S1-spectra, giving a proof of a connectedness conjecture of Voevodsky. The homotopy coniveau tower construction extends to a tower of functors on the Morel-Voevodsky stable homotopy category, and we identify this P1-stable homotopy coniveau tower with Voevodsky's slice filtration for P1-spectra. We also show that the 0th layer for the motivic sphere spectrum is the motivic cohomology spectrum, which gives the layers for a general P1-spectrum the structure of a module over motivic cohomology. This recovers and extends recent results of Voevodsky on the 0th layer of the slice filtration, and yields a spectral sequence that is reminiscent of the classical Atiyah-Hirzebruch spectral sequence.