On the slice spectral sequence

The Homotopy Coniveau Filtration

We examine the “homotopy coniveau tower” for a general cohomology theory on smooth k-schemes, satisfying some natural axioms, and give a new proof that the layers of this tower for K-theory agree with motivic cohomology. We show how these constructions lead to a tower of functors on the Morel-Voevodsky stable homotopy category, and identify this stable homotopy coniveau tower with Voevodsky’s s...

The Slice Spectral Sequence of Mackey Functors for the C4 Analog of Real K-theory

The purpose of this paper is to describe the slice spectral sequence of a 32-periodic C4-spectrum KH (to be defined below in §6, specifically Definition 6.3) related to the C4 norm (defined in [HHRa, §2.2.3]) MU ((C4)) = N4 C2MUR of the real cobordism spectrum MUR. Part of this spectral sequence is illustrated in an unpublished poster produced in late 2008 and shown in Figure 1. It shows the sp...

THE SLICE SPECTRAL SEQUENCE FOR RO(Cpn)-GRADED SUSPENSIONS OF HZ I

A new family in the stable homotopy groups of spheres

Let $p$ be a prime number greater than three. In this paper, we prove the existence of a new family of homotopy elements in the stable homotopy groups of spheres $pi_{ast}(S)$ which is represented by $h_nh_mtilde{beta}_{s+2}in {rm Ext}_A^{s+4, q[p^n+p^m+(s+2)p+(s+1)]+s}(mathbb{Z}_p,mathbb{Z}_p)$ up to nonzero scalar in the Adams spectral sequence, where $ngeq m+2>5$, $0leq sExt}_A^{s+2,q[(s+2)p...

The Homotopy Coniveau Tower

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 S 1-spectra, giving a proof of a connect-edness conjecture of Voevodsky. The homotopy coniveau tower construction extends to a...