On the K-theory of fields. (English) Zbl 0705.19004

Grayson, Daniel R.

Algebraic \(K\)-theory and algebraic number theory, Proc. Semin., Honolulu/Hawaii 1987, Contemp. Math. 83, 31-55 (1989).

[For the entire collection see Zbl 0655.00010.]
This is a very nice survey of the algebraic aspects of some recent results on the algebraic K-theory of fields. Particular attention is paid to the Merkur’ev-Suslin theorem and the K-theory of algebraically closed fields. For some of the theorems, the author provides brief sketches of proofs. Whenever appropriate, the author has also brought out the main points. Warnings are used as substitutes when the going becomes tough.

Reviewer: C.-H.Sah

MSC:

19Fxx	\(K\)-theory in number theory
11R70	\(K\)-theory of global fields
18F25	Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
19-02	Research exposition (monographs, survey articles) pertaining to \(K\)-theory
12G99	Homological methods (field theory)

Keywords:

Merkur’ev-Suslin theorem; K-theory of algebraically closed fields

Citations:

Zbl 0655.00010