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

Abstract

We prove that in the graded commutative ring $K_{\ast }(\mathbb{S})$, all positive degree elements are multiplicatively nilpotent. The analogous statements also hold for $T{C}_{\ast }(\mathbb{S};{\mathbb{Z}}_p^{\wedge })$ and $K_{\ast }(\mathbb{Z})$.

References in corpus (1)

• Homotopy-theoretically enriched categories of noncommutative motives

Cited by in corpus (1)

• The homotopy groups of the algebraic K-theory of the sphere spectrum