On two-primary algebraic K-theory of quadratic number rings with focus on K_2

Abstract

We give explicit formulas for the 2-rank of the algebraic K-groups of quadratic number rings. A 4-rank formula for K2 of quadratic number rings given in [1] provides further information about the actual group structure. The K2 claculations are based on 2- and 4-rank formulas for Picard groups of quadratic number fields. These formulas are derived in a completely elementary way from the classical 2-rank formula for the narrow ideal class group of a quadratic number field. We also lift the K2 results to higher algebraic K-groups.