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Simplicial schemes and Adams operations. (English) Zbl 0969.55008
Bass, H. (ed.) et al., Algebraic \(K\)-theory and its applications. Proceedings of the workshop and symposium, ICTP, Trieste, Italy, September 1-19, 1997. Singapore: World Scientific. 437-449 (1999).
Working in the homotopy category of schemes over a scheme \(S=\text{Spec }A\) due to J. F. Jardine [Can. J. Math. 39, 733-747 (1987; Zbl 0645.18006)] an algebraic \(K\)-theory spectrum is constructed by a method parallel to that of Segal for topological \(K\)-theory. Adams operations are constructed in the associated \(K\)-theory of schemes and extended to simplicial schemes; a \(\lambda\)-ring structure is also defined on the rational version of the latter.
For the entire collection see [Zbl 0949.00018].

MSC:
55S25 \(K\)-theory operations and generalized cohomology operations in algebraic topology
19E08 \(K\)-theory of schemes
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