Computing the tame kernel of quadratic imaginary fields

Jerzy Browkin, with an appendix by Karim Belabas, Herbert Gangl
2000 Mathematics of Computation  
J. Tate has determined the group K 2 O F (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. Ska lba for d = −19 and d = −20. In the present paper we discuss the methods of Qin and Ska lba, 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 K
more » ... ir computation of K 2 O F for some other values of d. The results agree with the conjectural structure of K 2 O F given in the paper by Browkin and Gangl.
doi:10.1090/s0025-5718-00-01182-0 fatcat:lfrkgruurzewzgofrsxuesotum