Computing the tame kernel of quadratic imaginary fields

Browkin, Jerzy; Belabas, Karim; Gangl, Herbert

Abstract

J. Tate has determined the group K2script O signF (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. Skałba for d = -19 and d = -20. In the present paper we discuss the methods of Qin and Skałba, 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 K2script O signF for some other values of d. The results agree with the conjectural structure of K2script O signF given in the paper by Browkin and Gangl.

Citation

Browkin, J., Belabas, K., & Gangl, H. (2000). Computing the tame kernel of quadratic imaginary fields. Mathematics of Computation, 69(232), 1667-1683. https://doi.org/10.1090/s0025-5718-00-01182-0

• Journal Article Type: Article
• Online Publication Date: Mar 15, 2000
• Publication Date: Jan 1, 2000
• Deposit Date: Mar 6, 2025
• Journal: Mathematics of Computation
• Print ISSN: 0025-5718
• Electronic ISSN: 1088-6842
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 69
• Issue: 232
• Pages: 1667-1683
• DOI: https://doi.org/10.1090/s0025-5718-00-01182-0
• Public URL: https://durham-repository.worktribe.com/output/3681384