Generators and Relations for K_2 O_F

Belabas, K.; Gangl, H.

Abstract

Tate's algorithm for computing K_2 O_F for rings of integers in a number field has been adapted for the computer and gives explicit generators for the group and sharp bounds on their order---the latter, together with some structural results on the p-primary part of K_2 O_F due to Tate and Keune, gives a proof of its structure for many number fields of small discriminants, confirming earlier conjectural results. For the first time, tame kernels of non-Galois fields are obtained.

Citation

Belabas, K., & Gangl, H. (2004). Generators and Relations for K_2 O_F. K-Theory, 31(3), 195 - 231. https://doi.org/10.1023/b%3Akthe.0000028979.91416.00

• Journal Article Type: Article
• Publication Date: 2004-03
• Deposit Date: Apr 24, 2007
• Journal: K-Theory
• Print ISSN: 0920-3036
• Electronic ISSN: 1573-0514
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 31
• Issue: 3
• Pages: 195 - 231
• DOI: https://doi.org/10.1023/b%3Akthe.0000028979.91416.00
• Keywords: K_2, Number fields, Tame kernel.