#### Volume 21, issue 6 (2017)

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The nilpotence theorem for the algebraic $K$–theory of the sphere spectrum

### Andrew J Blumberg and Michael A Mandell

Geometry & Topology 21 (2017) 3453–3466
##### Abstract

We prove that in the graded commutative ring ${K}_{\ast }\left(\mathbb{S}\right)$, all positive degree elements are multiplicatively nilpotent. The analogous statements also hold for ${TC}_{\ast }{\left(\mathbb{S}\right)}_{p}^{\wedge }$ and ${K}_{\ast }\left(ℤ\right)$.

##### Keywords
algebraic $K$–theory of spaces, nilpotence theorem, $p$–adic $L$–function
Primary: 19D10