On the slice spectral sequence
نویسندگان
چکیده
We introduce a variant of the slice spectral sequence which uses only regular slice cells, and state the precise relationship between the two spectral sequences. We analyze how the slice filtration of an equivariant spectrum that is concentrated over a normal subgroup is related to the slice filtration of its geometric fixed points, and use this to prove a conjecture of Hill on the slice filtration of an Eilenberg–Mac Lane spectrum [3]. We also show how the (co)connectivity of a spectrum results in the (co)connectivity of its slice tower, demonstrating the “efficiency” of the slice spectral sequence.
منابع مشابه
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...
متن کاملThe 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 Part of this spectral sequence is illustrated in an unpublished poster produced in late 2008 and shown in Figure 1.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...
متن کاملA 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...
متن کاملThe 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...
متن کامل