Higher algebraic \(K\)-theory: an overview
This book consists of five papers based on lectures delivered in 1985. It is intended as an introduction to the literature of higher algebraic \(K\)- theory; proofs are often omitted. The five papers are: Introduction to algebraic \(K\)-theory (\textit{Emilio Lluis-Puebla}), Introduction to algebraic \(K\)-theory and cyclic homology (\textit{Jean-Louis Loday}), Comparing algebraic and topological \(K\)-theory (\textit{Henri Gillet}), Algebraic \(K\)-theory of the integers (\textit{Christopher Soulé}), Applications of group cohomology to bilinear forms (\textit{Victor Snaith}). The first paper covers the homology of groups and the low-dimensional \(K\)-theory of rings. The second paper covers the algebraic \(K\)-theory and cyclic homology of rings; a more comprehensive version will appear in \textit{J.-L. Loday's} book: Cyclic homology (Springer Verlag, Grundlehren der mathematischen Wissenschaften) (to appear). The third part covers topological \(K\)-theory and the algebraic \(K\)-theory of varieties and schemes. It concludes with a proof of Suslin's rigidity theorem. The fourth part is mainly devoted to connections with the Bernoulli numbers. The fifth part contains material on group cohomology, Galois cohomology and the Hasse-Witt characteristic classes of bilinear forms. There are new proofs of results of Serre and Fröhlich. There is also a summary of work of \textit{V. Snaith} [Topology 27, 119-127 (1988; Zbl 0696.12012)].
algebraic \(K\)-theory of varieties and schemes
Hasse-Witt characteristic classes of bilinear forms
scientific article; zbMATH DE number 52853