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


18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
19D99 Higher algebraic \(K\)-theory


Zbl 0628.55011
Full Text: DOI


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