Relative reciprocities on Dedekind domains and the K_2 of a field, by Frans Keune

The author's proof in 1974 of Matsumoto's presentation of the K2 of a field was based on Bass' description of the SK1 of an ideal in a Dedekind domain by relative reciprocities together with a reciprocity law for the Milnor ring of a field. Here it is shown that with the use of general exact sequences in algebraic K-theory this description of the SK1 of an ideal in a Dedekind domain is easily derived. A proof of Matsumoto's theorem that does not use the Milnor ring is given here as well.


Frans Keune <keune@math.ru.nl>