Computing the tame kernel of quadratic imaginary fields

J. Tate has determined the group K2OF (called the tame kernel) for six quadratic imaginary number fields F = Q( d), where d = -3, -4, -7, -8, -11, -15. Modifying the method of Tate, H. Qin has done the same for d = -24 and d = -35, and M. Skalba for d = -19 and d = -20. In the present paper we discuss the methods of Qin and Skalba, and we apply our results to the field Q( -23). In the Appendix at the end of the paper K. Belabas and H. Gangl present the results of their computation of K2OF for some other values of d. The results agree with the conjectural structure of K2OF given in the paper by Browkin and Gangl.

• Type: Journal
• Year: 2000
• Where: MOC
• Authors: Jerzy Browkin, Karim Belabas, Herbert Gangl
• Keywords: MOC 2000, Quadratic Imaginary Number, Tame Kernel, Tate