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On the Generation of the Tame Kernel by Dennis-Stein Symbols

✍ Scribed by M. Geijsberts

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
416 KB
Volume
50
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let (p) be an odd prime number and let (F) be a number field not containing a primitive (p) th root of unity (\zeta_{p}). In this paper we show that if (\left.p\right}[F: \mathbb{Q}] \cdot \operatorname{disc}(F)) then the (p)-primary part of (K_{2}\left(C_{F}[1 / p]\right)) is generated by Dennis-Stein symbols. For the real quadratic fields (F=\mathbb{Q}(\sqrt{29})) and (F=\mathbb{Q}(\sqrt{109})) we compute generators for the tame kernel (K_{2}\left(\mathcal{C}{F}\right)) and give presentations for (S L{n}\left(\mathcal{C}_{F}\right)(n \geqslant 3)) for both fields.
c. 1995 Academic Press, Inc.

πŸ“œ SIMILAR VOLUMES

On the 4-rank of the Tame Kernel K2(O) i
On the 4-rank of the Tame Kernel K2(O) in Positive Definite Terms
✍ P.E. Conner; Jurgen Hurrelbrink πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 178 KB

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