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The K–theory presheaf of spectra

John F Jardine

Geometry & Topology Monographs 16 (2009) 151–178

DOI: 10.2140/gtm.2009.16.151

Abstract

This paper presents a relatively simple construction of the algebraic K–theory presheaf of spectra, which starts with a method of functorially associating a symmetric spectrum K(M) to an exact category M.

Some applications are displayed: these include a Galois cohomological descent spectral sequence for the étale K–theory of a scheme (where the Galois group is the Grothendieck fundamental group), and the Morel–Voevodsky description of Thomason–Trobaugh K–theory as Nisnevich K–theory in nonnegative degrees. The is also a spectrum-level description of Voevodsky’s periodicity operator for Nisnevich K–theory.

Keywords

spectra, algebraic K-theory, presheaf

Mathematical Subject Classification

Primary: 18F25, 55P42

Secondary: 18F20, 19E20

References
Publication

Received: 20 August 2008
Revised: 19 April 2009
Accepted: 20 April 2009
Published: 16 June 2009

Authors
John F Jardine
Department of Mathematics
University of Western Ontario
London, ON N6A5B7
Canada
http://www.math.uwo.ca/~jardine