Algebraic K-theory and twisted reciprocity laws, by Bruno Kahn

We extend the classical reciprocity laws of algebraic number theory to higher odd K-groups of algebraic integers. Moreover, we show that a suitable renormalisation of the corresponding ``twisted Legendre symbols" is independent ``in the average" from the chosen prime when the number field considered is Galois over Q. This seems new even in the classical case.


Bruno Kahn <kahn@math.jussieu.fr>