2013/02/28 by Rune Haugseng, Haynes Miller
Mathematics · #Abelian category #Abelian group #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Commutative property #Functor #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Multiplicative function #Nilpotent #Pure mathematics #Sequence (biology) #Spectral sequence #Spectrum (functional analysis) #math.AT #msc:18G40 #msc:55P47
paper · pdf · doi:10.2140/agt.2016.16.2911
published as Algebr. Geom. Topol. 16 (2016) 2911-2947 · 36 pages, v2: substantially rewritten, with a stronger version of the main result, v3: accepted version
openalex publication_date 2016/11/07 · arxiv created 2020/10/31 · arxiv updated 2020/11/03 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
We study the mod-2 cohomology spectral sequence arising from delooping the Bousfield-Kan cosimplicial space giving the 2-nilpotent completion of a connective spectrum X . Under good conditions its E 2 -term is computable as certain nonabelian derived functors evaluated at H .X / as a module over the Steenrod algebra, and it converges to the cohomology of 1 X . We provide general methods for computing the E 2 -term, including the construction of a multiplicative spectral sequence of Serre type for cofibration sequences of simplicial commutative algebras. Some simple examples are also considered; in particular, we show that the spectral sequence collapses at E 2 when X is a suspension spectrum.