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

Blumberg, Andrew; Mandell, Michael

doi:10.2140/gt.2017.21.3453

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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

DOI: 10.2140/gt.2017.21.3453

Abstract

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

Keywords

algebraic $K$–theory of spaces, nilpotence theorem, $p$–adic $L$–function

Mathematical Subject Classification 2010

Primary: 19D10

References

Publication

Received: 2 November 2015

Revised: 11 January 2017

Accepted: 18 February 2017

Published: 31 August 2017

Proposed: Mark Behrens

Seconded: Peter Teichner, Ralph Cohen

Authors

Andrew J Blumberg
Department of Mathematics University of Texas Austin, TX United States

Michael A Mandell
Department of Mathematics Indiana University Bloomington, IN United States

Volume 21, issue 6 (2017)