On tame kernel and class group in terms of quadratic forms

JOURNAL OF NUMBER THEORY

卷:96

Article

Yue, Q

关键词: the tame kernel;    class group;    genus theory;    unramified cyclic degree 4 extension;   

DOI  :  10.1006/jnth.2002.2808

来源: Elsevier

【 摘 要 】

The paper is to investigate the structure of the tame kernel K2OF for certain quadratic number fields F, which extends the scope of Conner and Hurrelbrink (J. Number Theory 88 (2001), 263 282). We determine the 4-rank and the 8-rank of the tame kernel, the Tate kernel, and the 2-part of the class group. Our characterizations are in terms of binary quadratic forms X-2 + 32 Y, X-2 + 64 Y-2, X-2 + 2p Y-2,2X(2) + p Y-2, X-2 - 2p Y-2, 2X(2) - p Y-2. The results are very useful for numerical computations. (C) 2002 Elsevier Science (USA).

【 授权许可】

Free