Letter from Tate to Iwasawa on a relation between \(K_2\) and Galois cohomology. (English) Zbl 0284.12004

Algebraic \(K\)-Theory II, Proc. Conf. Battelle Inst. 1972, Lect. Notes Math. 342, 524-527 (1973).
The \(l\)-primary part of \(K_2F\), \(F\) an algebraic number field, can be described in terms of the Galois cohomology of \(F\) provided one knows the \(\mathbb Z_l\)-rank of a particular cohomology group. In this letter the author shows that this rank can be determined by using Iwasawa’s theory of \(\mathbb Z_l\)-extensions.
For the entire collection see Zbl 0265.00008.


11R70 \(K\)-theory of global fields
11R34 Galois cohomology
11R23 Iwasawa theory
19C99 Steinberg groups and \(K_2\)


Zbl 0265.00008