On the 4-rank of the Tame Kernel K2(O) in Positive Definite Terms

✍ Scribed by P.E. Conner; Jurgen Hurrelbrink

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 178 KB
• Volume: 88
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.2000.2626

✦ Synopsis

The paper is about the structure of the tame kernel K 2 (O) for certain quadratic number fields. There has been recent progress in making explicit the 4-rank of the tame kernel of quadratic number fields and even in obtaining results about the 8-rank. The emphasis of this paper is to determine the 4-rank of the tame kernel in definite terms. Our characterizations are in terms of positive definite binary quadratic forms X 2 +32Y 2 , X 2 +2pY 2 , 2X 2 + pY 2 over Z. The results make numerical computations readily available, and the characterizations might generate some interest in ``density results'' concerning the 4-rank of tame kernels.