The nilpotence theorem for the algebraicK–theory of the sphere spectrum

2014/05/23 by Andrew J. Blumberg, Michael A. Mandell
Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic number #Algebraic structures and combinatorial models #Commutative property #Commutative ring #Degree (music) #Discrete mathematics #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Nilpotent #Physics #Pure mathematics #Ring (chemistry) #Spectrum (functional analysis) #Wedge (geometry) #math.AT #math.KT #msc:19D10

paper · pdf · doi:10.2140/gt.2017.21.3453

published as Geom. Topol. 21 (2017) 3453-3466

arxiv created 2014/05/23 · openalex publication_date 2017/08/31 · arxiv updated 2018/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove that in the graded commutative ring [math] , all positive degree elements are multiplicatively nilpotent. The analogous statements also hold for [math] and [math] .

Citations

• Higher algebraic K-theory: I
• Localization for THH(ku) and the topological Hochschild and cyclic homology of Waldhausen categories
• Class fields of abelian extensions of Q
• Algebraic K-theory of spaces
• Stable real cohomology of arithmetic groups
• Introduction to Cyclotomic Fields