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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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(S), all positive degree elements are multiplicatively nilpotent. The analogous statements also hold for TC(S)p and K().

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