Tame and wild kernels of quadratic imaginary number fields

Abstract

For all quadratic imaginary number fields F F of discriminant d > − 5000 , d>-5000, we give the conjectural value of the order of Milnor’s group (the tame kernel) K 2 O F , K_{2}O_{F}, where O F O_{F} is the ring of integers of F . F. Assuming that the order is correct, we determine the structure of the group K 2 O F K_{2}O_{F} and of its subgroup W F W_{F} (the wild kernel). It turns out that the odd part of the tame kernel is cyclic (with one exception, d = − 3387 d=-3387 ).