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Exterior power operations on higher K-theory. (English) Zbl 0701.18007
The author constructs lambda operations in the K-theory of exact categories with suitable notions of exterior powers, for instance categories of vector bundles on schemes. More generally, if \(M_ 0,M_ 1,..\). is a suitable sequence of categories with operations \(\bigwedge^ k: M_ n\to M_{nk}\), then he constructs operations \(\lambda^ k: K_*M_ n\to K_*M_{nk}\). The method is simplicial; it uses the construction of K-theory given by H. Gillet and D. Grayson [Ill. J. Math. 31, 574-597 (1987; Zbl 0628.55011)]. Thus the method avoids the plus-construction, which works only for the algebraic K-theory of rings.
Reviewer: R.J.Steiner

MSC:
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
19D99 Higher algebraic \(K\)-theory
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[1] H. Gillet and D. Grayson, On the loop space of the Q-construction, Illinois J. Math. 31 (1987), 574-597. · Zbl 0628.55011
[2] H. Gillet and C. Soulé, K-théorie et nullité des multiplicités d’intersection, C. R. Acad. Sc. Paris 300 (1985), 71-74.
[3] Alexander Grothendieck, La théorie des classes de Chern, Bull. Soc. Math. France 86 (1985), 137-154. · Zbl 0091.33201
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[5] Ch. Kratzer, ?-Structure en K-théorie algébrique, Comment. Math. Helv. 55 (1980), 233-254. · Zbl 0444.18008 · doi:10.1007/BF02566684
[6] Friedhelm Waldhausen, Algebraic K-theory of generalized free products, Annals of Math. 108 (1978), 135-256. · Zbl 0397.18012 · doi:10.2307/1971165
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