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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
##### Keywords:
simplicial scheme; $$K$$-theory; Adams operation