Geodesic
$K$-theory as an Eilenberg-Mac Lane spectrum
Documenta mathematica, Alexander S. Merkurjev's Sixtieth Birthday (2015), pp. 335-365.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

For an additive Waldhausen category linear over a ring $k$, the corresponding $K$-theory spectrum is a module spectrum over the $K$-theory spectrum of $k$. Thus if $k$ is a finite field of characteristic $p$, then after localization at $p$, we obtain an Eilenberg-MacLane spectrum -- in other words, a chain complex. We propose an elementary and direct construction of this chain complex that behaves well in families and uses only methods of homological algebra (in particular, the notions of a ring spectrum and a module spectrum are not used).
Classification : 19D50, 13D15
Keywords: Waldhausen $K$-theory, Eilenberg-MacLane spectrum 
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     author = {Kaledin, D.},
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Kaledin, D. $K$-theory as an Eilenberg-Mac Lane spectrum. Documenta mathematica, Alexander S. Merkurjev's Sixtieth Birthday (2015), pp. 335-365. http://geodesic.mathdoc.fr/item/DOCMA_2015__S2__a12/