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8-Ranks ofK2of Rings of Integers in Quadratic Number Fields

✍ Scribed by A. Vazzana

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
156 KB
Volume
76
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let F be a quadratic extension of Q and O F the ring of integers in F. A result of Tate enables one to compute the 2-rank of K 2 O F in terms of the 2-rank of the class group. Formulas for the 4-rank of K 2 O F exist, but are more involved. We give upper and lower bounds on the 8-rank of K 2 O F in terms of the narrow class group. In certain cases the upper and lower bounds agree, and the 8-rank of K 2 O F is exactly the 8-rank of the narrow class group. We then give a family of fields for which this equality holds.

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